Displaying similar documents to “Regularity of weak solutions to certain degenerate elliptic equations”

Weak solutions for elliptic systems with variable growth in Clifford analysis

Yongqiang Fu, Binlin Zhang (2013)

Czechoslovak Mathematical Journal

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In this paper we consider the following Dirichlet problem for elliptic systems: D A ( x , u ( x ) , D u ( x ) ) ¯ = B ( x , u ( x ) , D u ( x ) ) , x Ω , u ( x ) = 0 , x Ω , where D is a Dirac operator in Euclidean space, u ( x ) is defined in a bounded Lipschitz domain Ω in n and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the...

Finite volume schemes for fully non-linear elliptic equations in divergence form

Jérôme Droniou (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the p -laplacian kind: - div ( | u | p - 2 u ) = f (with 1 < p < ). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

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.