Displaying similar documents to “On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with L 1 data.”

Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems

Arina A. Arkhipova (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.

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.

Gradient estimates for elliptic systems in Carnot-Carathéodory spaces

Giuseppe Di Fazio, Maria Stella Fanciullo (2002)

Commentationes Mathematicae Universitatis Carolinae

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Let X = ( X 1 , X 2 , ⋯ , X q ) be a system of vector fields satisfying the Hörmander condition. We prove L X 2 , λ local regularity for the gradient X u of a solution of the following strongly elliptic system - X α * ( a i j α β ( x ) X β u j ) = g i - X α * f i α ( x ) ∀ i = 1 , 2 , ⋯ , N , where a i j α β ( x ) are bounded functions and belong to Vanishing Mean Oscillation space.