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Dirichlet problem for anisotropic prescribed mean curvature equation on unbounded domains.
- Source :
-
Journal of Mathematical Analysis & Applications . Jul2016, Vol. 439 Issue 2, p709-724. 16p. - Publication Year :
- 2016
-
Abstract
- In this paper, we consider the Dirichlet problem for hypersurfaces M = graph u of anisotropic prescribed mean curvature H = H ( x , u , N ) on unbounded domain Ω, where N is the unit normal to M at ( x , u ) . As a corollary of the result, we obtain the existence of translating solutions to the mean curvature flow with a forcing term on unbounded domains. The approach used here is a modified version of classical Perron's method, where the solutions to minimal surface equation are used as supersolutions and a family of auxiliary functions is constructed as local subsolutions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 439
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 113908910
- Full Text :
- https://doi.org/10.1016/j.jmaa.2016.03.009