Existence of a capillary surface with prescribed contact angle in $M\times\R$

Maria Calle; Leili Shahriyari

Existence of a capillary surface with prescribed contact angle in $M\times\R$

Analysis of PDEs 2014-06-05 v3 Differential Geometry

Authors: Maria Calle , Leili Shahriyari

Abstract

We study the prescribed mean curvature equation with a prescribed boundary contact angle condition in $M\times\R$ where $M^n$ is a Riemannian submanifold in $\R^{n+1}$ . The main purpose is to establish a priori gradient estimates for solutions, from which the long time existence of the solution are derived.

Keywords

capillary surface prescribed mean curvature contact angle gradient estimate long time existence Riemannian submanifold

Cite

@article{arxiv.1012.5490,
  title  = {Existence of a capillary surface with prescribed contact angle in $M\times\R$},
  author = {Maria Calle and Leili Shahriyari},
  journal= {arXiv preprint arXiv:1012.5490},
  year   = {2014}
}

Comments

This paper has been withdrawn by the author due to a crucial error in Lemma 2.1.1

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