无界区域上一类系数无界的线性抛物型微分方程的Cauchy-Dirichlet问题

G. Rubio
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引用次数: 8

摘要

考虑一类线性抛物型偏微分方程的Cauchy-Dirichlet问题。我们假设它是一个具有正则边界的无界开连通集。我们的假设是无界的,局部Lipschitz系数,不一定可微,具有连续数据和局部一致椭圆性。利用有界区域上的随机微分方程和抛物型微分方程构造了非齐次Cauchy-Dirichlet问题的经典解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Cauchy-Dirichlet Problem for a Class of Linear Parabolic Differential Equations with Unbounded Coefficients in an Unbounded Domain
We consider the Cauchy-Dirichlet problem in for a class of linear parabolic partial differential equations. We assume that is an unbounded, open, connected set with regular boundary. Our hypotheses are unbounded and locally Lipschitz coefficients, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution to the nonhomogeneous Cauchy-Dirichlet problem using stochastic differential equations and parabolic differential equations in bounded domains.
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