The inhomogeneous boundary Harnack principle for fully nonlinear and $p$-Laplace equations

Mark Allen; Dennis Kriventsov; Henrik Shahgholian

doi:10.4171/aihpc/40

JournalsaihpcVol. 40, No. 1pp. 133–156

The inhomogeneous boundary Harnack principle for fully nonlinear and $p$ -Laplace equations

Mark Allen
Brigham Young University, Provo, United States of America
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Dennis Kriventsov
Rutgers University, Piscataway, United States of America
- MathSciNet
- zbMATH Open
Henrik Shahgholian
KTH Royal Institute of Technology, Stockholm, Sweden

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Abstract

We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and $p$ -Laplace-type equations with a right-hand side, as well as for the Laplace equation on nontangentially accessible domains under extra conditions. The approach is completely new and gives a systematic approach for proving similar results for a variety of equations and geometries.

Cite this article

Mark Allen, Dennis Kriventsov, Henrik Shahgholian, The inhomogeneous boundary Harnack principle for fully nonlinear and $p$ -Laplace equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 1, pp. 133–156

DOI 10.4171/AIHPC/40