Estimates for parabolic equations with measure data in generalized Morrey spaces

Chao Zhang

doi:10.1142/S021919971850044X

Estimates for parabolic equations with measure data in generalized Morrey spaces

Chao Zhang^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, we prove the optimal generalized Morrey estimates for the spatial gradient of the solutions obtained by limits of approximations (SOLA) for a class of parabolic problems with right-hand side measure in a very general irregular domain. The nonlinearity is assumed to be merely measurable only in the time variable t and belongs to the small bounded mean oscillation (BMO) class as functions of the spatial variable x.

Original language	English
Article number	1850044
Journal	Communications in Contemporary Mathematics
Volume	21
Issue number	5
DOIs	https://doi.org/10.1142/S021919971850044X
State	Published - 1 Aug 2019

Keywords

Parabolic equation
Reifenberg flat domain
generalized Morrey spaces
gradient estimate
measure data problem

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10.1142/S021919971850044X

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title = "Estimates for parabolic equations with measure data in generalized Morrey spaces",

abstract = "In this paper, we prove the optimal generalized Morrey estimates for the spatial gradient of the solutions obtained by limits of approximations (SOLA) for a class of parabolic problems with right-hand side measure in a very general irregular domain. The nonlinearity is assumed to be merely measurable only in the time variable t and belongs to the small bounded mean oscillation (BMO) class as functions of the spatial variable x.",

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AB - In this paper, we prove the optimal generalized Morrey estimates for the spatial gradient of the solutions obtained by limits of approximations (SOLA) for a class of parabolic problems with right-hand side measure in a very general irregular domain. The nonlinearity is assumed to be merely measurable only in the time variable t and belongs to the small bounded mean oscillation (BMO) class as functions of the spatial variable x.

KW - Parabolic equation

KW - Reifenberg flat domain

KW - generalized Morrey spaces

KW - gradient estimate

KW - measure data problem

UR - https://www.scopus.com/pages/publications/85052942522

U2 - 10.1142/S021919971850044X

DO - 10.1142/S021919971850044X

M3 - 文章

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SN - 0219-1997

VL - 21

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 5

M1 - 1850044

ER -

Estimates for parabolic equations with measure data in generalized Morrey spaces

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Keywords

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