New Results for p Harmonic Functions

John L. Lewis, Kaj Nyström

Type: Article

Publication Date: 2011-01-01

Citations: 9

DOI: https://doi.org/10.4310/pamq.2011.v7.n2.a4

Abstract

In this paper we first discuss new results of the authors concerning a boundary Harnack inequality and Hölder continuity up to the boundary for the ratio of two positive p harmonic functions, 1 < p < ∞, which vanish on a portion of a Lipschitz domain.Second we discuss applications of these results to the Martin boundary problem for p harmonic functions and to certain boundary regularity -free boundary problems.

Locations

Pure and Applied Mathematics Quarterly - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Boundary behavior and the Martin boundary problem for<i>p</i>harmonic functions in Lipschitz domains	2010	John L. Lewis Kaj Nyström
+ PDF Chat	Boundary Harnack principle and Martin boundary for a uniform domain	2001	Hiroaki Aikawa
+	Boundary behaviour of p-harmonic functions in domains beyond Lipschitz domains	2008	John L. Lewis Kaj Nyström
+ PDF Chat	Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains	2007	John L. Lewis Kaj Nyström
+	Hölder estimates of p-harmonic extension operators	2005	Hiroaki Aikawa Nageswari Shanmugalingam
+	A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with Lipschitz Boundary Values	2016	Nikos Katzourakis
+	A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with Lipschitz Boundary Values	2016	Nikos Katzourakis
+ PDF Chat	The boundary Harnack inequality for variable exponent $$p$$ p -Laplacian, Carleson estimates, barrier functions and $${p(\cdot )}$$ p ( · ) -harmonic measures	2015	Tomasz Adamowicz Niklas L. P. Lundström
+ PDF Chat	A remark on global W^{1,p} bounds for harmonic functions with Lipschitz boundary values	2017	Nikos Katzourakis
+	A condition equivalent to the Holder continuity of harmonic functions on unbounded Lipschitz domains	2025	Marijan Marković
+	A note on higher regularity boundary Harnack inequality	2015	D. De Silva Ovidiu Savin
+ PDF Chat	Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces	2006	Anders Björn Jana Björn
+	A note on higher regularity boundary Harnack inequality	2014	Daniela De Silva Ovidiu Savin
+	A note on higher regularity boundary Harnack inequality	2014	Daniela De Silva Ovidiu Savin
+ PDF Chat	Boundary Harnack inequalities for operators of 𝑝-Laplace type in Reifenberg flat domains	2008	John L. Lewis Niklas L. P. Lundström Kaj Nyström
+	The boundary Harnack inequality for variable exponent $p$-Laplacian, Carleson estimates, barrier functions and $p(\cdot)$-harmonic measures	2014	Tomasz Adamowicz Niklas L. P. Lundström
+	Applications of Boundary Harnack Inequalities for p Harmonic Functions and Related Topics	2012	Jessica B. Lewis
+ PDF Chat	Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains	1978	Jang-Mei Wu
+	Regularity of Lipschitz free boundaries in two-phase problems for the p-Laplace operator	2010	John L. Lewis Kaj Nyström
+ PDF Chat	The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in R^n and metric spaces	2015	Daniel Hansevi

Works That Cite This (8)

Action	Title	Year	Authors
+	The Hadamard variational formula and the Minkowski problem for p-capacity	2015	Andrea Colesanti Kaj Nyström Paolo Salani Jie Xiao Da Yang G. Zhang
+ PDF Chat	Regularity of flat free boundaries in two-phase problems for the p-Laplace operator	2011	John L. Lewis Kaj Nyström
+	Regularity of Lipschitz free boundaries in two-phase problems for the p-Laplace operator	2010	John L. Lewis Kaj Nyström
+	Estimates for solutions to equations of p -Laplace type in Ahlfors regular NTA-domains	2014	Benny Avelin Kaj Nyström
+ PDF Chat	Regularity and free boundary regularity for the $p$-Laplace operator in Reifenberg flat and Ahlfors regular domains	2011	John L. Lewis Kaj Nyström
+ PDF Chat	Quasi-linear PDEs and low-dimensional sets	2018	John L. Lewis Kaj Nyström
+ PDF Chat	On the dimension of $p$-harmonic measure in space	2013	John L. Lewis Kaj Nyström Andrew Vogel
+ PDF Chat	The spherical p-harmonic eigenvalue problem in non-smooth domains	2017	Konstantinos T. Gkikas Лаурент Верон

Works Cited by This (7)

Action	Title	Year	Authors
+	REGULARITY AND FREE BOUNDARY REGULARITY FOR THE p LAPLACIAN IN LIPSCHITZ AND C1 DOMAINS	2008	John L. Lewis Kaj Nyström
+ PDF Chat	Harmonic measure on locally flat domains	1997	Carlos E. Kenig Tatiana Toro
+ PDF Chat	Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains	2007	John L. Lewis Kaj Nyström
+ PDF Chat	Poisson kernel characterization of Reifenberg flat chord arc domains	2003	Carlos E. Kenig Tatiana Toro
+	Boundary behavior of harmonic functions in non-tangentially accessible domains	1982	David Jerison Carlos E. Kenig
+ PDF Chat	The Lp-integrability of the partial derivatives of A quasiconformal mapping	1973	F. W. Gehring
+ PDF Chat	Free Boundary Regularity for Harmonic Measures and Poisson Kernels	1999	Carlos E. Kenig Tatiana Toro