Equivalence of viscosity and weak solutions for the normalized 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: Calculus of Variations and Partial Differential Equations
سال: 2018
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-018-1375-1