Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs

Fuente: arXiv

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Detalles Bibliográficos
Autores principales:	Verma, Ram Baran, Mallick, Mohan
Formato:	Preprint
Publicado:	2024
Materias:	Analysis of PDEs Primary: 35K10, 35K20, Secondary: 35K10, 35K20
Acceso en línea:	Acceder al recurso
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

_version_	1866909217676328960
author	Verma, Ram Baran Mallick, Mohan
author_facet	Verma, Ram Baran Mallick, Mohan
contents	This article investigates the exceptional set of the boundary for the following problem: \begin{equation} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{λ,Λ}^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \rm{in} ~ Ω_{T}, \end{aligned} \end{equation} We provide a sufficient condition on the exceptional set in terms of the bound of the Hausdorff measure of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.
format	Preprint
id	arxiv_https___arxiv_org_abs_2406_03481
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs Verma, Ram Baran Mallick, Mohan Analysis of PDEs Primary: 35K10, 35K20, Secondary: 35K10, 35K20 This article investigates the exceptional set of the boundary for the following problem: \begin{equation} \begin{aligned} -\frac{\partial u}{\partial t} + \mathcal{M}_{λ,Λ}^+(D^2u) + b(x,t)\cdot Du + c(x,t)u =0 \quad \rm{in} ~ Ω_{T}, \end{aligned} \end{equation} We provide a sufficient condition on the exceptional set in terms of the bound of the Hausdorff measure of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.
title	Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs
topic	Analysis of PDEs Primary: 35K10, 35K20, Secondary: 35K10, 35K20
url	https://arxiv.org/abs/2406.03481

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