Displaying similar documents to “Solvability of the Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains.”

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.

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...

The Dirichlet problem for elliptic equations in the plane

Paola Cavaliere, Maria Transirico (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper an existence and uniqueness theorem for the Dirichlet problem in W 2 , p for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class .