# Boyarsky–Meyers Estimate for Solutions to Zaremba Problem

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### Article Info

DATE

2022-06-29

AUTHORS ABSTRACT

The variational solution to the Zaremba problem for a divergent linear second order elliptic equation with measurable coefficients is considered. The problem is set in a local Lipschitz graph domain. An estimate in L2+δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{2+\delta }$$\end{document}, δ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta >0$$\end{document}, for the gradient of a solution, is proved. An example of the problem with the Dirichlet data supported by a fractal set of zero (n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n-1)$$\end{document}-dimensional measure and non-zero p-capacity, p>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>1$$\end{document} is constructed. More... »

PAGES

1197-1211

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-022-01805-0

DOI

http://dx.doi.org/10.1007/s00205-022-01805-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1149066683

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