Geodesic
Anisotropic problems with variable exponents and constant Dirichlet conditions
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study a general class of anisotropic problems involving $\vec p(\cdot)$-Laplace type operators. We search for weak solutions that are constant on the boundary by introducing a new subspace of the anisotropic Sobolev space with variable exponent and by proving that it is a reflexive Banach space. Our argumentation for the existence of weak solutions is mainly based on a variant of the mountain pass theorem of Ambrosetti and Rabinowitz.
Classification : 35J25, 46E35, 35D30, 35J20
Keywords: anisotropic variable exponent Sobolev spaces, Dirichlet problem, existence of weak solutions, mountain pass theorem 
@article{EJDE_2013__2013__a75,
     author = {Boureanu, Maria-Magdalena and Udrea, Cristian and Udrea, Diana-Nicoleta},
     title = {Anisotropic problems with variable exponents and constant {Dirichlet} conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a75/}
}
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Boureanu, Maria-Magdalena; Udrea, Cristian; Udrea, Diana-Nicoleta. Anisotropic problems with variable exponents and constant Dirichlet conditions. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a75/