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Teoremi di media e formole di maggiorazione relative alle funzioni biarmoniche

Gaetano Fichera (1978)

Rendiconti del Seminario Matematico della Università di Padova

The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Carlos E. Kenig (1984/1985)

Séminaire Équations aux dérivées partielles (Polytechnique)

The multiple layer potential for the biharmonic equation in $n$ variables

Alberto Cialdea (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The definition of multiple layer potential for the biharmonic equation in $R^{n}$ is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.

The obstacle problem for the biharmonic operator

Luis A. Caffarelli, Avner Friedman (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The simple layer potential for the biharmonic equation in $n$ variables

Alberto Cialdea (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A theory of the «simple layer potential» for the classical biharmonic problem in $R^{n}$ is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with $n$ scalar components into a vector whose components are $n$ differential forms of degree one.

Thinness and non-tangential limit associated to coupled PDE

Allami Benyaiche, Salma Ghiate (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. $▵^{2} ϕ = 0$ ) and equations of $▵^{2} ϕ = ϕ$ type.