Displaying similar documents to “On general solvability properties of p -Lapalacian-like equations”

Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case q = 3 d d + 2

Jörg Wolf (2007)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider weak solutions 𝐮 : Ω d to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain Ω d ( d = 2 or d = 3 ). For the critical case q = 3 d d + 2 we prove the higher integrability of 𝐮 which forms the basis for applying the method of differences in order to get fractional differentiability of 𝐮 . From this we show the existence of second order weak derivatives of u .

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let u be a weak solution of a quasilinear elliptic equation of the growth p with a measure right hand term μ . We estimate u ( z ) at an interior point z of the domain Ω , or an irregular boundary point z Ω , in terms of a norm of u , a nonlinear potential of μ and the Wiener integral of 𝐑 n Ω . This quantifies the result on necessity of the Wiener criterion.

The Neumann problem for some degenerate elliptic equations

Albo Carlos Cavalheiro (2006)

Applications of Mathematics

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In the paper we study the equation L u = f , where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set Ω . We prove existence and uniqueness of solutions in the space H ( Ω ) for the Neumann problem.

On a class of nonlinear problems involving a p ( x ) -Laplace type operator

Mihai Mihăilescu (2008)

Czechoslovak Mathematical Journal

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We study the boundary value problem - d i v ( ( | u | p 1 ( x ) - 2 + | u | p 2 ( x ) - 2 ) u ) = f ( x , u ) in Ω , u = 0 on Ω , where Ω is a smooth bounded domain in N . Our attention is focused on two cases when f ( x , u ) = ± ( - λ | u | m ( x ) - 2 u + | u | q ( x ) - 2 u ) , where m ( x ) = max { p 1 ( x ) , p 2 ( x ) } for any x Ω ¯ or m ( x ) < q ( x ) < N · m ( x ) ( N - m ( x ) ) for any x Ω ¯ . In the former case we show the existence of infinitely many weak solutions for any λ > 0 . In the latter we prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a 2 -symmetric version for even...