Displaying similar documents to “Existence and estimates of Green's function for degenerate elliptic equations”

Area integral estimates for higher order elliptic equations and systems

Björn E. J. Dahlberg, Carlos E. Kenig, Jill Pipher, G. C. Verchota (1997)

Annales de l'institut Fourier

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Let L be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in L p norm between the maximal function and the square function of solutions to L in Lipschitz domains. Several applications of this result are discussed.

Existence and properties of the Green function for a class of degenerate parabolic equations.

José C. Fernandes, Bruno Franchi (1996)

Revista Matemática Iberoamericana

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It is known that degenerate parabolic equations exhibit somehow different phenomena when we compare them with their elliptic counterparts. Thus, the problem of existence and properties of the Green function for degenerate parabolic boundary value problems is not completely solved, even after the contributions of [GN] and [GW4], in the sense that the existence problem is still open, even if the a priori estimates proved in [GN] will be crucial in our approach (...).

Higher regularity for nonlinear oblique derivative problems in Lipschitz domains

Gary M. Lieberman (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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There is a long history of studying nonlinear boundary value problems for elliptic differential equations in a domain with sufficiently smooth boundary. In this paper, we show that the gradient of the solution of such a problem is continuous when a directional derivative is prescribed on the boundary of a Lipschitz domain for a large class of nonlinear equations under weak conditions on the data of the problem. The class of equations includes linear equations with fairly rough coefficients...