Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2023; 60(2): 495-505

Online first article March 16, 2023      Printed March 31, 2023

https://doi.org/10.4134/BKMS.b220243

Copyright © The Korean Mathematical Society.

A note on comparison principle for elliptic obstacle problems with $L^{1}$-data

Kyeong Song, Yeonghun Youn

Seoul National University; Yeungnam University

Abstract

In this note, we study a comparison principle for elliptic obstacle problems of $p$-Laplacian type with $L^1$-data. As a consequence, we improve some known regularity results for obstacle problems with zero Dirichlet boundary conditions.

Keywords: Obstacle problem, regularity theory, comparison principle

MSC numbers: 35B51, 35B65, 35J87, 35R05

Supported by: This work was supported by NRF-2020R1C1C1A01009760.