Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach
B. Franchi, R. Serapioni (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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B. Franchi, R. Serapioni (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Björn E. J. Dahlberg, Carlos E. Kenig, Jill Pipher, G. C. Verchota (1997)
Annales de l'institut Fourier
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Let be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in norm between the maximal function and the square function of solutions to in Lipschitz domains. Several applications of this result are discussed.
Gary M. Lieberman (1994)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Neil S. Trudinger (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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 (...).
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...