Geodesic
Anisotropic problems with variable exponents and constant Dirichlet conditions
Electronic journal of differential equations, Tome 2013 (2013)
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},
     year = {2013},
     volume = {2013},
     zbl = {1288.35223},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a75/}
}
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AU  - Udrea,  Cristian
AU  - Udrea,  Diana-Nicoleta
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JO  - Electronic journal of differential equations
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VL  - 2013
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%A Udrea,  Cristian
%A Udrea,  Diana-Nicoleta
%T Anisotropic problems with variable exponents and constant Dirichlet conditions
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a75/
%G en
%F EJDE_2013__2013__a75
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/