Displaying similar documents to “Liouville results for m -Laplace equations of Lane-Emden-Fowler type”

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

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Let Ω be a bounded open subset of ℝ n , n > 2 . In Ω we deduce the global differentiability result u ∈ H 2 ( Ω , ℝ N ) for the solutions u ∈ H 1 ( Ω , ℝ n ) of the Dirichlet problem u - g ∈ H 0 1 ( Ω , ℝ N ) , - ∑ i D i a i ( x , u , D u ) = B 0 ( x , u , D u ) with controlled growth and nonlinearity q = 2 . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.

A positive solution for an asymptotically linear elliptic problem on ℝ N autonomous at infinity

Louis Jeanjean, Kazunaga Tanaka (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on ℝ N . The main difficulties to overcome are the lack of a priori bounds for Palais–Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be...

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.