Displaying similar documents to “Existence of solutions for a nonlinear elliptic equation with general flux term.”

Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data

Alberto Fiorenza, Alain Prignet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the sequence u n , which is solution of - div ( a ( x , 𝔻 u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of 𝐑 N and u n = 0 on ∂ Ω , when f n tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N -function Φ , and prove a non-existence result.

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.