Equivalence of viscosity and weak solutions for the p(x)-Laplacian
نویسندگان
چکیده
منابع مشابه
EQUIVALENCE OF VISCOSITY AND WEAK SOLUTIONS FOR THE p(x)-LAPLACIAN
We consider different notions of solutions to the p(x)-Laplace equation − div(|Du(x)| Du(x)) = 0 with 1 < p(x) < ∞. We show by proving a comparison principle that viscosity supersolutions and p(x)-superharmonic functions of nonlinear potential theory coincide. This implies that weak and viscosity solutions are the same class of functions, and that viscosity solutions to Dirichlet problems are u...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2010
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2010.09.004