Lorentz-Morrey regularity for nonlinear elliptic problems withirregular obstacles over Reifenberg flat domains

Sun-Sig Byun; Yumi Cho

doi:10.3934/dcds.2015.35.4791

Article Contents

2015, Volume 35, Issue 10: 4791-4804. Doi: 10.3934/dcds.2015.35.4791

This issue Previous Article Rigorous numerics for nonlinear operators with tridiagonal dominant linear part Next Article Schrödinger equations with rough Hamiltonians

Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains

Sun-Sig Byun^1, and
Yumi Cho^2,

1.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747
2.
School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722

Received: July 31, 2014

Revised: January 31, 2015

Published: September 2015

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Abstract

A global Calderón-Zygmund estimate type estimate in Weighted Lorentz spaces and Lorentz-Morrey spaces is obtained for weak solutions to elliptic obstacle problems of $p$-Laplacian type with discontinuous coefficients over Reifenberg flat domains.

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Mathematics Subject Classification: Primary: 35J87; Secondary: 35R05, 35J60, 35B65, 46E35.

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