Geodesic
Equivalence of viscosity and weak solutions for the p(x)-Laplacian
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 6, pp. 1471-1487

Voir la notice de l'article provenant de la source 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.

DOI : 10.1016/j.anihpc.2010.09.004
Classification : 35J92, 35D40, 31C45, 35B60
Keywords: Comparison principle, Viscosity solutions, Uniqueness, $ p(x)$-Superharmonic functions, Radó type theorem, Removability 
@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},
     pages = {1471--1487},
     publisher = {Elsevier},
     volume = {27},
     number = {6},
     year = {2010},
     doi = {10.1016/j.anihpc.2010.09.004},
     mrnumber = {2738329},
     zbl = {1205.35136},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.09.004/}
}
TY  - JOUR
AU  - Juutinen, Petri
AU  - Lukkari, Teemu
AU  - Parviainen, Mikko
TI  - Equivalence of viscosity and weak solutions for the $ p(x)$-Laplacian
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2010
SP  - 1471
EP  - 1487
VL  - 27
IS  - 6
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.09.004/
DO  - 10.1016/j.anihpc.2010.09.004
LA  - en
ID  - AIHPC_2010__27_6_1471_0
ER  - 
%0 Journal Article
%A Juutinen, Petri
%A Lukkari, Teemu
%A Parviainen, Mikko
%T Equivalence of viscosity and weak solutions for the $ p(x)$-Laplacian
%J Annales de l'I.H.P. Analyse non linéaire
%D 2010
%P 1471-1487
%V 27
%N 6
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.09.004/
%R 10.1016/j.anihpc.2010.09.004
%G en
%F 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) no. 6, pp. 1471-1487. doi: 10.1016/j.anihpc.2010.09.004

Cité par Sources :