Dirichlet and Neumann boundary values of solutions to higher order elliptic equations

Ariel Barton, Steve Hofmann, Svitlana Mayboroda

Type: Article

Publication Date: 2019-01-01

Citations: 7

DOI: https://doi.org/10.5802/aif.3278

Abstract

We show that if u is a solution to a linear elliptic differential equation of order 2m≥2 in the half-space with t-independent coefficients, and if u satisfies certain area integral estimates, then the Dirichlet and Neumann boundary values of u exist and lie in a Lebesgue space L p (ℝ n ) or Sobolev space W ˙ ±1 p (ℝ n ). Even in the case where u is a solution to a second order equation, our results are new for certain values of p.

Locations

arXiv (Cornell University) - View - PDF
French digital mathematics library (Numdam) - View - PDF
Annals of the Fourier Institute (Institut Fourier) - View - PDF
Annales de l’institut Fourier - View - PDF

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+ PDF Chat	Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain	1980	Björn Dahlbert
+	Function spaces on subsets of Rn	1984	Alf Jonsson Hans Wallin Jaak Peetre
+ PDF Chat	Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients	2016	Ariel Barton
+ PDF Chat	The method of layer potentials in<i>L<sup>p</sup></i>and endpoint spaces for elliptic operators with<i>L<sup>∞</sup></i>coefficients	2015	Steve Hofmann Marius Mitrea Andrew J. Morris
+ PDF Chat	Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition	2016	Martin Dindoš Jill Pipher David Rule
+	Equivalence between Regularity Theorems and Heat Kernel Estimates for Higher Order Elliptic Operators and Systems under Divergence Form	2000	Pascal Auscher Mahmoud Qafsaoui
+	The neumann problem for elliptic equations with non-smooth coefficients	1993	Carlos E. Kenig Jill Pipher
+ PDF Chat	Positive harmonic functions on Lipschitz domains	1970	Richard A. Hunt Richard L. Wheeden
+	Analyticity of layer potentials and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> solvability of boundary value problems for divergence form elliptic equations with complex <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msup><mml:mi>L</mml:mi><mml:mo>∞</mml:mo></mml:msup></mml:math> coefficients	2010	M. Angeles Alfonseca Pascal Auscher Andreas Axelsson Steve Hofmann Seick Kim
+	Construction of a singular elliptic-harmonic measure	1980	Luciano Modica Stefano Mortola