The classical solvability of the contact angle problem for generalized equations of mean curvature type
type: Item
instance of: scholarly article
title: The classical solvability of the contact angle problem for generalized equations of mean curvature type
zbMATH Open document ID: 1255.35122
DOI: 10.4171/PM/1916
author: Pierre-Etienne Druet
published in: Portugaliae Mathematica. Nova Série
publication date: 2012-12-06T00:00:00Z
review text: Summary: Mean curvature equations of general quasilinear type in connection with contact-angle boundary conditions are considered in this paper. We investigate the existence, uniqueness and continuous dependence of the solution in classical function spaces. On the one hand, a survey of techniques and ideas developed in the 1970s and 1980s, mainly by Uraltseva, is presented. On the other hand, extensions of these results are also proposed: we formulate growth conditions for the general dependence of the potential on the \(x_{N+1}\)-variable, and we extend the existence and uniqueness statements to this case. Moreover, the regularity assumptions on the right-hand side are relaxed, and alternative proofs for the higher-order estimates and the existence result are provided.
Mathematics Subject Classification ID: 35J93
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 58J99
zbMATH DE Number: 6113254
zbMATH Keywords: generalized mean curvature equation
zbMATH Keywords: contact-angle problem
zbMATH Keywords: classical solvability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6113254