Equivalence of viscosity and weak solutions for the p(x)-Laplacian
Juutinen, Petri ; Lukkari, Teemu ; Parviainen, Mikko
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 1471-1487 / Harvested from Numdam

We consider different notions of solutions to the p(x)-Laplace equation - div Du(x)| p(x)-2 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 unique. As an application, we prove a Radó type removability theorem.

Publié le : 2010-01-01
DOI : https://doi.org/10.1016/j.anihpc.2010.09.004
Classification:  35J92,  35D40,  31C45,  35B60
@article{AIHPC_2010__27_6_1471_0,
     author = {Juutinen, Petri and Lukkari, Teemu and Parviainen, Mikko},
     title = {Equivalence of viscosity and weak solutions for the $ p(x)$-Laplacian},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {27},
     year = {2010},
     pages = {1471-1487},
     doi = {10.1016/j.anihpc.2010.09.004},
     mrnumber = {2738329},
     zbl = {1205.35136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2010__27_6_1471_0}
}
Juutinen, Petri; Lukkari, Teemu; Parviainen, Mikko. Equivalence of viscosity and weak solutions for the $ p(x)$-Laplacian. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) pp. 1471-1487. doi : 10.1016/j.anihpc.2010.09.004. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_6_1471_0/

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