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 → ℝ d to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain Ω ⊂ ℝ 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.