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Sobolev spaces

Nonlinear wavelet density estimation for biased data in Sobolev spaces

Nonlinear wavelet density estimation for biased data in Sobolev spaces

... In this paper, we consider the nonlinear hard thresholding wavelet density estimation for biased data in Sobolev spaces WrN N ∈ N+.. We mainly give the upper bound of minimax rate of con[r] ...

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Uniform rotundity in every direction of Orlicz Sobolev spaces

Uniform rotundity in every direction of Orlicz Sobolev spaces

... Orlicz-Sobolev spaces. Analyzing and combining the properties of both Orlicz spaces and Sobolev spaces, we get the sufficient and necessary criteria for Orlicz-Sobolev ...

10

Hölder Quasicontinuity in Variable Exponent Sobolev Spaces

Hölder Quasicontinuity in Variable Exponent Sobolev Spaces

... where p is a function of x. The exact definition is presented below, see also [1, 2]. Variable exponent Sobolev spaces have been used in the modeling of electrorheological fluids, see, for example, [3–7] ...

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Local existence for the non resistive MHD equations in nearly optimal Sobolev spaces

Local existence for the non resistive MHD equations in nearly optimal Sobolev spaces

... In the scale of Sobolev spaces we suspect that the result that we have proved here is optimal. Bourgain and Li [3] showed that the Euler equations on R d are ill posed in H 1 + d / 2 for n = 2, 3, and we ...

16

Generalizations of Troisi’s inequality in weighted p Sobolev spaces with singularities

Generalizations of Troisi’s inequality in weighted p Sobolev spaces with singularities

... Considering the pivotal role of Troisi’s inequality in studying such kinds of singular anisotropic elliptic equations like (1.5) (e.g., see the results in our upcoming papers), we need, in the first place, to deduce it ...

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Solvability of the Dirichlet Problem for Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

Solvability of the Dirichlet Problem for Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

... This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of R n , n ≥ 3.. We [r] ...

13

Parabolic Equations in Musielak-Orlicz-Sobolev Spaces

Parabolic Equations in Musielak-Orlicz-Sobolev Spaces

... Musielak-Orlicz-Sobolev spaces (see Theorem 1), as it is done in the setting of Orlicz-Sobolev spaces (see [12]), which allows us, on the one hand, to regularize a test function by smooth ones ...

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An Eulerian–Lagrangian form for the Euler equations in Sobolev spaces

An Eulerian–Lagrangian form for the Euler equations in Sobolev spaces

... estimates, which may seem more familiar to some readers. We have given two different iteration schemes to deduce well-posedness using these estimates; iterating with respect to u is natural in this setting and leads to a ...

14

A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces

A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces

... This paper is devoted to characterizing nonhomogeneous wavelet dual frames in Sobolev spaces pairs H s Rd , H –s Rd via a pair of equations.. Before proceeding, we introduce some notion[r] ...

8

Extreme points and rotundity of Orlicz Sobolev spaces

Extreme points and rotundity of Orlicz Sobolev spaces

... that Sobolev spaces have played essential roles in solving nonlinear par- tial differential ...Orlicz-Sobolev spaces are generalized from Sobolev ...Sobolev spaces. A ...

7

Square functions related to integral of Marcinkiewicz and Sobolev spaces

Square functions related to integral of Marcinkiewicz and Sobolev spaces

... We prove a characterization of Sobolev spaces of order 2 by square functions related to the integral of Marcinkiewicz.. Littlewood-Paley functions, Sobolev spaces.[r] ...

16

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

... We investigate the existence of solutions of the Kirchhoff elliptic equations with nonlinearity in R N . Using the ideas developed in Orlicz spaces and the technique of variation principle, we prove that there are ...

13

Differential equations of divergence form in separable Musielak-Orlicz-Sobolev spaces

Differential equations of divergence form in separable Musielak-Orlicz-Sobolev spaces

... can be omitted because of the reflexivity of the Musielak-Orlicz-Sobolev spaces in []. We refer to some results of sub-supersolution methods for variational inequalities and the existence of solutions for ...

19

Boundedness on Hardy Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels

Boundedness on Hardy Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels

... We will give the definitions for Sobolev spaces and Hardy-Sobolev spaces, and prove the key lemma Lemma 2.2 for Bessel functions in the next section. The proof of Theorem 1.2 will be given in ...

17

Multiplicity of solutions for singular semilinear elliptic equations in weighted Sobolev spaces

Multiplicity of solutions for singular semilinear elliptic equations in weighted Sobolev spaces

... In , Shapiro [] studied a series of eigenvalue problems of singular quasilinear el- liptic and parabolic equations in weighted Sobolev spaces, he obtained many existence results by using Galerkin ...

14

On Solvability of p- harmonic Type Equations in Grand Sobolev Spaces

On Solvability of p- harmonic Type Equations in Grand Sobolev Spaces

... in Sobolev and grand Sobolev spaces were studied, ...grand Sobolev, Besov and Morrey type spaces were studied in [8, 9, 14–16, 18–23] and ...

8

Multiple solutions for non homogeneous degenerate Schrodinger equations in cone Sobolev spaces

Multiple solutions for non homogeneous degenerate Schrodinger equations in cone Sobolev spaces

... In Section 2, we will introduce the manifolds with conical singularities, the stretched manifold associated to the conic manifold, cone Sobolev spaces and the corresponding properties of them. In Section 3, ...

14

ON A ROBIN PROBLEM IN ORLICZ-SOBOLEV SPACES

ON A ROBIN PROBLEM IN ORLICZ-SOBOLEV SPACES

... Problem (1) is settled in Orlicz-Sobolev spaces and treated by variational approach and the main medium is Ekeland’s variational principle. In Section 2, we give the basic knowledge and preliminary results. ...

11

Multivariate box spline wavelets in higher dimensional Sobolev spaces

Multivariate box spline wavelets in higher dimensional Sobolev spaces

... In this paper, we have successfully generalized MRA over higher-dimensional Sobolev spaces by giving orthonormality and density conditions. Further, we constructed nonsep- arable orthonormal wavelets in a ...

14

The Poisson equation in homogeneous Sobolev spaces

The Poisson equation in homogeneous Sobolev spaces

... weighted Sobolev spaces directly [8, 13, 15], or it has first been multiplied by some weights and then solved in standard Sobolev spaces ...

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