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Journal of Differential Equations
Article
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Journal of Differential Equations
Article . 2002
License: Elsevier Non-Commercial
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Journal of Differential Equations
Article . 2002 . Peer-reviewed
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zbMATH Open
Article . 2002
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The Boundary Behavior of Heat Kernels of Dirichlet Laplacians

The boundary behavior of heat kernels of Dirichlet Laplacians
Authors: Zhang, Qi S.;

The Boundary Behavior of Heat Kernels of Dirichlet Laplacians

Abstract

It is obtained qualitative sharp description of heat kernel \(G\) of Dirichlet Laplacian on bounded \(C^{1,1}\) domain \(D.\) There exists positive constants \(c_1, c_2\) such that, for \(\rho(x)=\text{dist}(x,\partial D)\) \[ \left[{\rho(x)\rho(y)\over t}\wedge 1\right]{c_1\over t^{n/2} } e^{-c_2|x-y|^2/t} \leq G(x,t;y,0)\leq \left[{\rho(x)\rho(y)\over t}\wedge 1\right]{1\over c_1 t^{n/2} } e^{-|x-y|^2/(c_2t)} \] for all \(x,y\in D\) and \(0

Related Organizations
Keywords

upper and lower estimates, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Initial value problems for second-order parabolic equations, Analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
73
Top 10%
Top 10%
Average
hybrid