Embedding near domains

Near-Optimal Distributed Tree Embedding

Tree embeddings are a powerful tool in the area of graph approximation algorithms. Roughly speaking, they transform problems on general graphs into much easier ones on trees. Fakcharoenphol, Rao, and Talwar (FRT) [STOC’04] present a probabilistic tree embedding that transforms n-node metrics into (probability distributions over) trees, while stretching each pairwise distance by at most anO(log ...

Near-Optimal Search in Continuous Domains

We investigate search problems in continuous state and action spaces with no uncertainty. Actions have costs and can only be taken at discrete time steps (unlike the case with continuous control). Given an admissible heuristic function and a starting state, the objective is to find a minimum-cost plan that reaches a goal state. As the continuous domain does not allow the tight optimality result...

On Holomorphic Embedding of Planar Domains into C2

Lp Embedding and Nonlinear Eigenvalue Problems for Unbounded Domains

Let R denote real iV-dimensional Euclidean space. Then it is a well-known fact that the imbedding of the Sobolev space Wi,2(R) in LP(R ) is bounded for 2g>pS2N/(N-2), but is definitely not compact. Consequently the theory of critical points for general isoperimetric variational problems defined over arbitrary unbounded domains in R has been little investigated despite its importance. Indeed the...

Compactness of the Embedding Operators for Rough Domains

New classes of non-smooth bounded domains D, for which the embedding operator from H1(D) into L2(D) is compact, are introduced. These classes include, in particular, the domains whose boundary locally are graphs of C−functions, but also contain much larger classes of domains. Examples of non-smooth domains for which the above embedding is compact are given. Applications to scattering by rough o...