Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(4): 1123-1148

Printed July 31, 2016

https://doi.org/10.4134/BKMS.b150567

Copyright © The Korean Mathematical Society.

Note on local estimates for weak solution of boundary value problem for second order parabolic equation

Jongkeun Choi

Seoul National University

Abstract

The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

Keywords: De Giorgi estimate, boundedness estimate, H\"older estimate, Dirichlet boundary condition, Neumann boundary condition, measurable coefficients

MSC numbers: Primary 35K10, 35D30