Displaying similar documents to “Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients”

Some remarks on a class of weight functions

Loredana Caso, Maria Transirico (1996)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we obtain some results about a class of functions ρ : Ω → R + , where Ω is an open set of R n , which are related to the distance function from a fixed subset S ρ ⊂ ∂ Ω . We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function ρ .

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.