[PDF] Top 20 On the existence of minimal surfaces with free boundary

... Proof: Since the (PS)-Conditon is verified by the a -e n e r g y , Theorem 3.17 claims that the infimum o f this functional is achieved for all hom otopy classes o f maps in L*’^a (£)s . Since in the homotopy classes , ... See full document

... Here is the first application we wish to discuss: since we can fully classify bubbles and half-bubbles of Morse index less than two (see Corollary 22 and Corollary 24) we can then get novel, unconditional, geometric ... See full document

... There are classifications theorems that single out the flat equatorial disk and the critical catenoid among free boundary minimal surfaces in B 3 . Some of them will be reviewed in Section 2. ... See full document

... the existence of embedded minimal surfaces in ...desired minimal surface, such that 'SM has positive mean curvature; the condition of positive mean curvature is what is needed to apply one of ... See full document

... a free boundary value problem of the second-order ordinary differential equation in the velocity potential and established the global existence of solutions to the piston problem for unsteady ... See full document

... an existence theorem which will appear elsewhere [10], we show that incompressible maps flow for all time without the domain metric degenerating, and subconverge to a conformal harmonic ... See full document

... g, and h resp. b. Perhaps one of the more natural arguments to get the existence of time periodic solutions of problems of this type is to show the existence of a fixed point for the Poincar´e map. This was ... See full document

... of minimal Lagrangian embeddings we gave in ...equivariant minimal immersions into CH 2 (save for the Lagrangian examples whose existence is a consequence of the “mountain-pass” solutions to the ... See full document

... Abstract. The problem of the consolidation of an aerated fine powder under gravity is consid- ered. The industrial relevance of the problem is discussed and a mathematical model is introduced. The mathematical structure ... See full document

... two-sided free boundary minimal surfaces in mean convex domains of three-manifolds with non-negative scalar curvature must be topological disks or totally geodesic annuli (see for example ... See full document

... of free boundary minimal surfaces, starting from the special setting of Euclidean domains, goes back at least to Courant [9, 10] and has attracted considerable attention for several ...among ... See full document

... a free boundary and general logistic term in higher space dimensions and heterogeneous environment, which is used to describe the spreading of a new or invasive ...the existence and uniqueness of the ... See full document

... Since many free boundary problems and obstacle problems may be reduced to partial differential equations with discontinuous nonlinearities, the existence of multiple solu- tions for Diri[r] ... See full document

... of free boundary minimal surfaces, starting from the special setting of Euclidean domains, goes back at least to Courant [9, 10] and has attracted considerable attention for several ...among ... See full document

... the boundary ∂M is not fixed (like in Plateau’s problem) but subject to the sole constraint ∂M ⊂ ...of existence results have been obtained via surprisingly diverse methods (see, among others, ... See full document

... gomogennmedium . However, in a thin passivating layer on the strange base layer, these values  b and  b are not proved. Furthermore, the current values  b , b in the volume of the passivating layer, and its more ... See full document

... The study of impulsive dynamic equations on time scales has been initiated by Hender- son [4], Benchohra et al. [5], and Atici and Biles [6]. Extremal solutions of PBVP for im- pulsive differential equations and difference ... See full document

... Figure 1. A hexagonal lattice discretized by regular triangles. The total number of vertices N including those on the boundary is given by N = 91. This number is calculated by the formula N = 3L 2 + 3L + 1, where ... See full document

... approach as in the worst case scenario every simplex in C is in a relation which then requires iteration over all simplices and therefore does the same amount of work as the naive algorithm previously discussed. We now ... See full document

... that in this case polymer microsphere surfaces, performing sorption centres function of metal nanoparticles, allow to form stable dispersions. A disadvantage of this method is that photochemical reaction with the ... See full document