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Sobolev Embeddings for Generalized Ridged Domains
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This article is published in Proceedings of The London Mathematical Society.The article was published on 1987-01-01. It has received 94 citations till now. The article focuses on the topics: Sobolev space.read more
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Differential equations methods for the Monge-Kantorovich mass transfer problem
Lawrence C. Evans,Wilfrid Gangbo +1 more
TL;DR: In this paper, uniform estimates on the $p$-Laplacian, limits as $p\to\infty$ The transport set and transport rays Differentiability and smoothness properties of the potential Generic properties of transport rays Behavior of the transport density along rays Vanishing of the Transport density at the ends of rays Approximate mass transfer plans Passage to limits a.k.a. Optimality
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The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations†
Yanyan Li,Louis Nirenberg +1 more
TL;DR: In this paper, the distance function to the boundary, Finsler geometry and singular set of viscosity solutions of some Hamilton-Jacobi equations are studied, and the singular set is analyzed.
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The essential spectrum of Neumann Laplacians on some bounded singular domains
TL;DR: In this paper, the essential spectrum of the Neumann Laplacian on singular domains of the type "rooms and passages" or "combs" is determined from geometric data.
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The distance function from the boundary in a minkowski space
Graziano Crasta,Annalisa Malusa +1 more
TL;DR: In this paper, the Minkowski distance of a point from the boundary of a tubular neighborhood to the cut locus of a set of points of nondifferentiability has been shown to be the Jacobian determinant of the change of variables that associates to every point outside the locus.
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Fast/slow diffusion and collapsing sandpiles
TL;DR: In this paper, the authors regard the limit as p → ∞ of the flow governed by the p -Laplacian as providing a simplistic model for the collapse of an initially unstable sandpile.