On the Lipschitz regularity of solutions of a minimum problem with free boundary
type: Item
instance of: scholarly article
title: On the Lipschitz regularity of solutions of a minimum problem with free boundary
zbMATH Open document ID: 1147.35116
DOI: 10.4171/IFB/180
author: A. L. Karakhanyan
published in: Interfaces and Free Boundaries
publication date: 2008-07-21T00:00:00Z
review text: Summary: In this article under assumption of ``small'' density for negativity set, we prove local Lipschitz regularity for the one phase minimization problem with free boundary for the functional \[ {\mathcal E}_p(v,\Omega)=\int_\Omega [|\nabla v|^p+ \lambda^p_1\chi_{\{u\leq0\}}+\lambda^p_2 \chi_{\{u>0\}}],\quad 1<p<\infty, \] where \(\lambda_1, \lambda_2\) are positive constants so that \(\Lambda=\lambda_1^p-\lambda_2^p<0\), \(\chi_{D}\) is the characteristic function of set \(D\), \(\Omega\subset\mathbb R^n\) is (smooth) domain and minimum is taken over a suitable subspace of \(W^{1,p}(\Omega)\).
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5302267
zbMATH Keywords: two-phase minimization problem
zbMATH Keywords: free boundary
zbMATH Keywords: Lipschitz regularity
MaRDI profile type: Publication
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cites work: Q4354419
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description: scientific article; zbMATH DE number 5302267