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Existence of Weak Solutions for a Nonlocal Problem Involving the p(x) Laplace Operator

Existence of Weak Solutions for a Nonlocal Problem Involving the p(x) Laplace Operator

Keywords px-Laplace operator, p x-Kirchhoff-type equations, variable exponent Sobolev spaces, variational method, mountain pass theorem, Ekeland variational principle MSC: 35D05; 35J60; 3[r]

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Riesz Means of Dirichlet Eigenvalues for the Sub Laplace Operator on the Engel Group

Riesz Means of Dirichlet Eigenvalues for the Sub Laplace Operator on the Engel Group

Riesz Means of Dirichlet Eigenvalues for the Sub-Laplace Operator on the Engel Group Jingjing Xue Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China E[r]

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Positive solutions to n dimensional \(\alpha  {1}+\alpha  {2}\) order fractional differential system with p Laplace operator

Positive solutions to n dimensional \(\alpha {1}+\alpha {2}\) order fractional differential system with p Laplace operator

In this paper, we study an n-dimensional fractional differential system with p-Laplace operator, which involves multi-strip integral boundary conditions. By using the Leggett–Williams fixed point theorem, the existence results of at least three positive solutions are established. Besides, we also get the nonexistence results of positive solutions. Finally, two examples are presented to validate the main results.

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Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator

Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator

The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the p ( x )-Laplace operator with Neumann boundary condition. The technical approach is mainly based on a three critical points theorem due to Ricceri. MSC: 35D05; 35J60; 58E05.

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Absolute Monotonicity of Functions Related To Estimates of First Eigenvalue of Laplace Operator on Riemannian Manifolds

Absolute Monotonicity of Functions Related To Estimates of First Eigenvalue of Laplace Operator on Riemannian Manifolds

[12] P. Li and S. T. Yau, Estimates of eigenvalues of a compact Riemannian manifold, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), 205–239, Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980. [13] J. Ling, The first eigenvalue of a closed manifold with positive Ricci curvature, Proc. Amer.

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Existence Results for a Nonlocal Problem Involving the p Laplace Operator

Existence Results for a Nonlocal Problem Involving the p Laplace Operator

this reason some of the authors, in particular those who work in ODEs, call equations involving the p-Laplacian “half-linear” equations. The word “half-linear” reflects the fact that “one half” of the properties of linearity (i.e. additivity) is lost, while “one half” of the properties is preserved (i.e. homogeneity). The p-Laplace operator is very popular in nonlinear analysis and appears particularly in describing the behavior of compressible fluid in a homogeneous isotropic rigid porous medium (see e.g. [8, 12, 18]).

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12. Harmonic Analysis Associated with the Generalized
Dunkl-Bessel-Laplace Operator

12. Harmonic Analysis Associated with the Generalized Dunkl-Bessel-Laplace Operator

Mourou, Transmutation Operators Associated with a Bessel Type Op-erator on The Half Line and Certain of Their Applications, Tamsui Oxford Journal of Information and Mathematical Scienc[r]

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Constrained and unconstrained rearrangement minimization problems related to the p Laplace operator

Constrained and unconstrained rearrangement minimization problems related to the p Laplace operator

which is the one phase obstacle problem for the p-Laplacian operator. Through a private com- munication with H. Shahgholian, we found that many questions related to the free boundary of (3.19) are yet to be settled, see [11] and [13]. However, when p = 2, the free boundary of the problem (3.19) is extensively studied, see for example [15].

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9. A shape reconstruction problem with  the  Laplace operator

9. A shape reconstruction problem with the Laplace operator

In section 2, we establish the shape optimization results. And we prove the nec- essary conditions of optimality that is the existence of Lagrange multiplier.Section 3 is devoted to auxiliary lemmas based on maximum principal theory [24]. These lemmas play a fundamental part in the following sections. In section 4, we give, under geometrical assumptions, an uniqueness results which ensure the statement of an algorithm and its convergence. In the last section, we discuss on a general elliptical operator and we end by some classical numerical illustrations. But this numerical analysis gives interesting information and allows us to talk on futures.
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Direct and inverse problem for geometric perturbation of the Laplace operator in a strip

Direct and inverse problem for geometric perturbation of the Laplace operator in a strip

application related to the above model problem are described, for example, in [1, 11] (see also the references therein). Let us mention the articles [2, 5, 10, 15, 17] on the inverse boundary value problems for the Laplace equation in a bounded domain. Our problem presents additional difficulties related to the unbounded nature of the domain and, to our knowledge, it was not considered in the literature. In this work we generalize the potential method used in the precursor works of Kress and Rundel [9, 10].

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Improving the Sharpness of Digital Images Using a Modified Laplacian Sharpening Technique

Improving the Sharpness of Digital Images Using a Modified Laplacian Sharpening Technique

Abstract ⎯ Many imaging systems produce images with deficient sharpness due to different real limitations. Hence, various image sharpening techniques have been used to improve the acutance of digital images. One of such is the well-known Laplacian sharpening technique. When implementing the basic Laplacian technique for image sharpening, two main drawbacks were detected. First, the amount of introduced sharpness cannot be increased or decreased. Second, in many situations, the resulted image suffers from a noticeable increase in brightness around the sharpened edges. In this article, an improved version of the basic Laplacian technique is proposed, wherein it contains two key modifications of weighting the Laplace operator to control the introduced sharpness and tweaking the second order derivatives to provide adequate brightness for recovered edges. To perform reliable experiments, only real-degraded images were used, and their accuracies were measured using a specialized no-reference image quality assessment metric. From the obtained experimental results, it is evident that the proposed technique outperformed the comparable techniques in terms of recorded accuracy and visual appearance.
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Existence of multiple positive solutions for nonhomogeneous fractional Laplace problems with critical growth

Existence of multiple positive solutions for nonhomogeneous fractional Laplace problems with critical growth

positive minimal solution for all γ ∈ (0, γ ∗ ] and admits no positive solution for γ > γ ∗ . We prove Theorem 1.1 by the method of monotonic iteration, also known as the super and subsolution method, which is a basic tool in nonlinear partial differential equations. In this paper, we discuss a fractional Laplace operator version of this method compared with second order linear or quasilinear elliptic operator. With respect to the classical case of the Laplacian, here some estimates are more delicate, due to the non-local nature of the operator (–) s .
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On the spectrum of the negative Laplacian for general 
			doubly connected bounded domains

On the spectrum of the negative Laplacian for general doubly connected bounded domains

This paper is devoted to asymptotic formulas for functions related with the spectrum of the standard Laplace operator in two and three dimensional bounded doubly connected domains with i[r]

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Estimates for Resonant Frequencies Under Boundary Deformation in Multi-dimensional Space

Estimates for Resonant Frequencies Under Boundary Deformation in Multi-dimensional Space

and Lamberti have developed in [13] some preliminary abstract results for the dependence of the eigenvalues upon perturbation. Their applications to the Dirichlet eigenvalue problem for the Laplace operator appear clearly in Section 3 of their paper and in Theorem 3.21 when they justify the analyticity result for some symmetric functions of eigenvalues. Our analysis and uniform asymptotic formulas of the eigenfunctions, which are represented by the single-layer potential involving the Green function, are considerably different from those in [12, 13, 10]. Next, Our method differ, essentially, from the classical methods used to study the analytic dependence of the eigenfunctions of a real or complex parameter and used to give the asymp- totic formulae for the eigenvalues.
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Schrödinger Operators on Graphs and Branched Manifolds

Schrödinger Operators on Graphs and Branched Manifolds

In this paper we describe the set of all Schrödinger operators on graph and branched manifold, defined as a self-adjoint extension of the operator, originally defined on smooth functions with supports, not contained in the branch points manifold. Thus, given a description of the various options, we determine the Laplace operator on the space of the functions defined on a branched manifold. Description of the definition of each of the self-ad- joint extensions is given in terms of linear relations satisfied by the limit at the branch points and the boundary points of the graph function value in the domain of operator and the its derivative. Each of the Laplace operators corresponds to the Markov process, whose behavior in a neighborhood of branch points, we determined by the choice of the domain of the Laplace operator, obtained in this paper results, which is an extension of the study work [8] describes the self-adjoint extensions of a graph with a single vertex and two edges, to the case of a graph with an arbitrary number of edges. In addition, this paper summarizes the results of [6] in the case of Lap- lace operators, for which the linear relation in the space of boundary values that define the domain of the opera- tor, do not admit the possibility of expressing the limit function values at the boundary points and branch points of the graph of the limiting values of its derivative.
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Operator theory on spectrum of discrete laplace beltrami operator riemannian metric

Operator theory on spectrum of discrete laplace beltrami operator riemannian metric

Laplace – Beltrami operator plays a fundamental role in Riemannian geometric .In real applications, smooth metric surface is usually represented as triangulated mesh the manifold heat kernel is estimated from the discrete Laplace operator- Discrete Laplace – Beltrami operators on triangulated surface meshes span the entire spectrum of geometry processing applications including mesh parameterization segmentation. The Riemannian manifold with boundary, in the Euclidean domain the interior geometry is given, flat and trivial, and the interesting phenomena come from the shape of the boundary, Riemannian manifolds have no boundary, and the geometric phenomena are those of the interior. The present paper is an introduction, so we have to refrain from saying too must. To any compact Riemannian manifold (M,g) is boundary we associate second- order (P.D.E) , the Laplace operator  is defined by :  ( f )   div ( grad f ) for 2 ( , )
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Inversion theorem for distributional Fourier Laplace transform

Inversion theorem for distributional Fourier Laplace transform

n example is the Laplace transform, which renders a useful class of differential equations trivially solvable, converting them into algebraic ones instead. Another is the very well-known Fourier transform, which maps unctions of frequencies (Berian J. James, 2008). These transforms play an important role in the analysis of all kinds of physical phenomenon. As a link between the various applications of these transforms the authors

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Boundary value problems in time for wave equations on RN

Boundary value problems in time for wave equations on RN

Wave equation, radial symmetry, boundary value problem, eigenvalue problem, Hilbert space, weighted Sobolev space, Fredholm operator, Laplace transform, Bessel functions.. 1980 AMS SUBJE[r]

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Arc Image Processing Based on LabVIEW

Arc Image Processing Based on LabVIEW

The NI Vision Builder AI processing module has multiple edge detection functions such as Laplace edge detection operator, Prewitt edge detection operator, Sobel edge detection operator, and Robert edge detection operator. Among them, The characteristic of Laplace edge detection operator is that the edge detection is more continuous, accurate and clear, and the false edge is effectively avoided [11], therefore, this experiment uses this operator to process the arc image.

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Finite Time Engineering

Finite Time Engineering

The classical Laplace transform theory violates the requirements of modern engineering implementations. (a) We show that the ILT is valid only for infinite duration signals. On the other hand the modern engineering uses finite duration signals. (b) ILT models have poles; the FLT models do not generate poles. Thus ILT models may introduce instability in engineering implementations. (c) ILT requires convolution which is not valid for finite duration signals. (d) ILT methods are based on steady state concepts. Microprocessors do not see steady state in engineering implementations. (e) Infinite time theory for
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