Displaying similar documents to “Existence and localization results for p ( x ) -Laplacian via topological methods.”

Weak solutions for elliptic systems with variable growth in Clifford analysis

Yongqiang Fu, Binlin Zhang (2013)

Czechoslovak Mathematical Journal

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In this paper we consider the following Dirichlet problem for elliptic systems: D A ( x , u ( x ) , D u ( x ) ) ¯ = B ( x , u ( x ) , D u ( x ) ) , x ∈ Ω , u ( x ) = 0 , x ∈ ∂ Ω , where D is a Dirac operator in Euclidean space, u ( x ) is defined in a bounded Lipschitz domain Ω in ℝ n and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the...

Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis

Maria Alessandra Ragusa (1999)

Commentationes Mathematicae Universitatis Carolinae

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In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class H 0 1 , p ( Ω ) for all 1 < p < ∞ and, as a consequence, the Hölder regularity of the solution u . ℒ is an elliptic second order operator with discontinuous coefficients ( V M O ) and the lower order terms belong to suitable Lebesgue spaces.

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.