Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 9 of 9 for “"Convex domain"”.
-
Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2
… class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest …
-
The Illumination of Symmetric Spiky Balls and Cap Bodies; and a note on the Vertex Classification of Planar C-polygons
This thesis handles two problems in the field of convex geometry. The first, is the problem of illuminating the boundary of Euclidean shapes known as spiky balls and cap bodies in various dimensions. Specifically we consider illuminating the cases where a spiky ball is 2-illuminable, and the cases …
-
Computational Methods for Control of Queueing Models in Bounded Domains
… describe the dynamics on the boundary of closed, convex domain. Using relaxed stochastic controls we show that the approximating numerical solution converges to the actual solution as the size of the mesh in the discretized state space goes to zero, and illustrate with an example.
-
Regularity of Neumann solutions to an elliptic free boundary problem
… which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , in a weak sense. We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. …
-
Geometric Properties of the Ferrand Metric
… of an open Euclidean ball contained in a domain is convex with respect to the Ferrand metric. As a result, the arc-length parametrization of a Ferrand geodesic has Lipschitz continuous first derivative, and this result is sharp. We consider the Ferrand geometry of a convex domain. We show …
-
Generalized Characteristics Of A Generic Polytope
… curves of XH. When S is the boundary of a smooth convex domain K˜ ⊂ R 2n, then the least action among closed characteristics of LS is equal to the Ekeland-Hofer-Zehnder capacity, a symplectic invariant. From a result due to Artstein-Avidan and Ostrover, there exists a continuous extension of this …
-
Holomorphic Hardy Space Representations for Convex Domains in Cn
… with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are strongly convex with …
-
Asymptotically optimal shapes for counting lattice points and eigenvalues
… lattice points under a concave (or convex) curve with respect to reciprocal stretching in the coordinate directions. The optimal domain is shown to be asymptotically balanced, meaning that the optimal stretch factor approaches 1 as the ""radius"" approaches infinity. In particular, …
-
Combinatorial Problems with Geometric Flavour
… c_k\delta |A|$, where $\coo(A)$ is the smallest convex progression (convex set intersected with an affine sub-lattice) containing $A$. In particular, we deduce the sharp stability result for the Brunn--Minkowski inequality for equal sets, conjectured by Figalli and Jerison. Given $\delta>0$ …