Displaying similar documents to “Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems”

Existence of solutions of degenerated unilateral problems with L 1 data

Lahsen Aharouch, Youssef Akdim (2004)

Annales mathématiques Blaise Pascal

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In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type A u + g ( x , u , ∇ u ) = f - div F , where A is a Leray-Lions operator and g is a Carathéodory function having natural growth with respect to | ∇ u | and satisfying the sign condition. The second term is such that, f ∈ L 1 ( Ω ) and F ∈ Π i = 1 N L p ′ ( Ω , w i 1 - p ′ ) .

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n ∂ ∂ x n on ℝ n is proved. In this note there is shown that in the cases k ≠ 0 , k ≠ 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.

On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions

Joachim Naumann, Jörg Wolf, Michael Wolff (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove the interior Hölder continuity of weak solutions to parabolic systems ∂ u j ∂ t - D α a j α ( x , t , u , ∇ u ) = 0 in Q ( j = 1 , ... , N ) ( Q = Ω × ( 0 , T ) , Ω ⊂ ℝ 2 ), where the coefficients a j α ( x , t , u , ξ ) are measurable in x , Hölder continuous in t and Lipschitz continuous in u and ξ .