An infinity Laplace equation with gradient term and mixed boundary conditions

Scott N. Armstrong; Charles K. Smart; Stephanie J. Somersille

An infinity Laplace equation with gradient term and mixed boundary conditions

Analysis of PDEs 2009-10-29 v2

Authors: Scott N. Armstrong , Charles K. Smart , Stephanie J. Somersille

Abstract

We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation $-\Delta_\infty u - \beta |Du| = f,$ subject to Dirichlet or mixed Dirichlet-Neumann boundary conditions. Our arguments rely on comparing solutions of the PDE to subsolutions and supersolutions of a certain finite difference approximation.

Keywords

infinity laplace equation gradient term mixed boundary conditions existence uniqueness stability finite difference approximation

Cite

@article{arxiv.0910.3744,
  title  = {An infinity Laplace equation with gradient term and mixed boundary conditions},
  author = {Scott N. Armstrong and Charles K. Smart and Stephanie J. Somersille},
  journal= {arXiv preprint arXiv:0910.3744},
  year   = {2009}
}

Comments

13 pages, minor mistakes and typos corrected

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