Prescribed mean curvature equation on torus

Author:

Tsukamoto Yuki1

Affiliation:

1. Department of Mathematics , Tokyo Institute of Technology , 152-8551 , Tokyo , Japan

Abstract

Abstract Prescribed mean curvature problems on the torus have been considered in one dimension. In this paper, we prove the existence of a graph on the n-dimensional torus 𝕋 n {\mathbb{T}^{n}} , the mean curvature vector of which equals the normal component of a given vector field satisfying suitable conditions for a Sobolev norm, the integrated value, and monotonicity.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Reference14 articles.

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4. D. Denny, A unique solution to a nonlinear elliptic equation, J. Math. Anal. Appl. 365 (2010), no. 2, 467–482.

5. M. Feng, Periodic solutions for prescribed mean curvature Liénard equation with a deviating argument, Nonlinear Anal. Real World Appl. 13 (2012), no. 3, 1216–1223.

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