Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
type: Item
instance of: scholarly article
title: Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
zbMATH Open document ID: 0846.35040
DOI: 10.1007/BF02567822
published in: Manuscripta Mathematica
publication date: 1996-04-16T00:00:00Z
full work available at URL: https://eudml.org/doc/156127
review text: Consider elliptic systems of the form \[ - D_\alpha(A^{\alpha\beta}_{ij}(x) D_\beta u^j)= D_\alpha f^\alpha_i+ F_i\quad\text{in} \quad \Omega, \] where \(\Omega\) is a bounded \(C^1\) domain in \(\mathbb{R}^n\) and \(A^{\alpha \beta}_{ij}\in C^0(\overline\Omega)\). The authors prove the existence of a Green's matrix and establish optimal decay properties by deriving optimal estimates for the Green's function and its gradient in weak Lebesgue spaces through \(L^p\) estimates and interpolation theorems. Standard interior regularity estimates and scaling lead to pointwise estimates. A sharp comparison with the corresponding Green's matrix for systems with constant coefficients is also obtained.
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 35E05
zbMATH DE Number: 866167
zbMATH Keywords: Green's function
zbMATH Keywords: \(L^ p\) estimates
zbMATH Keywords: interpolation
author: Georg Dolzmann
author: Stefan Müller
reviewed by: Philip Schaefer
MaRDI profile type: Publication
cites work: Q5549343
cites work: The Green-matrix for elliptic systems which satisfy the Legendre-Hadamard condition
cites work: The Green matrix for strongly elliptic systems of second order with continuous coefficients
cites work: The Green function for uniformly elliptic equations
cites work: Q4084067
cites work: Some regularity results for quasilinear elliptic systems of second order
cites work: Q4123700
cites work: Q3228825
cites work: Q5725878
cites work: Q5518064
cites work: Q5607484
cites work: Q5640160
OpenAlex ID: W2081210755
description: scientific article; zbMATH DE number 866167