The Boundary Behavior of Heat Kernels of Dirichlet Laplacians
TLDR
In this article, a complete and qualitatively sharp description of heat kernels G of Dirichlet Laplacians on bounded C 1, 1 domains D is given, and the bounds when D is unbounded are also given.About:
This article is published in Journal of Differential Equations.The article was published on 2002-07-01 and is currently open access. It has received 137 citations till now. The article focuses on the topics: Bounded function & Boundary (topology).read more
Citations
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Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Journal ArticleDOI
Heat kernel estimates for the Dirichlet fractional Laplacian
TL;DR: In this article, the Dirichlet heat kernel of a non-local operator on open sets has been studied and sharp two-sided estimates for the heat kernel have been obtained for C 1.1 open sets.
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Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
TL;DR: In this paper, the authors give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.
Heat Kernel Estimates for Dirichlet Fractional Laplacian
Panki Kim,Zhen-Qing,Renming Song +2 more
TL;DR: In this paper, the authors considered the Dirichlet heat kernel of a non-local Laplacian operator on open sets and established sharp two-sided estimates for the heat kernel.
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Two-sided heat kernel estimates for censored stable-like processes
TL;DR: In this article, the exact behavior of the transition density functions of censored α-stable-like processes in C 1,1 open sets in R d, where d ≥ 1 and α ∈ (1,2) was studied.
References
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Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
Book
Heat kernels and spectral theory
TL;DR: In this paper, the authors introduce the concept of Logarithmic Sobolev inequalities and Gaussian bounds on heat kernels, as well as Riemannian manifolds.
Journal Article
Non-negative solutions of linear parabolic equations
TL;DR: In this article, the conditions générales d'utilisation (http://www.snsnsns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions generales d’utilisation, i.e., toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
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The Green function for uniformly elliptic equations
Michael Grüter,Kjell-Ove Widman +1 more
TL;DR: In this paper, a generalization of the usual Green function to equations with only measurable and bounded coefficients is discussed and the existence and uniqueness as well as several other important properties are shown such a Green function proves useful in connection with quasilinear elliptic systems of "diagonal type".
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