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Quasilinear elliptic equations with discontinuous coefficients

Lucio Boccardo, Giuseppe Buttazzo (1988)

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

We prove an existence result for equations of the form { - D i ( a i j ( x , u ) D j u ) = f in Ω u H 0 1 ( Ω ) . where the coefficients a i j ( x , s ) satisfy the usual ellipticity conditions and hypotheses weaker than the continuity with respect to the variable s . Moreover, we give a counterexample which shows that the problem above may have no solution if the coefficients a i j ( x , s ) are supposed only Borel functions

Quasilinear elliptic problems with multivalued terms

Nikolaos Halidias, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin’s critical point theory for lower semicontinuous energy functionals.

Quasi-minima

Mariano Giaquinta, Enrico Giusti (1984)

Annales de l'I.H.P. Analyse non linéaire

Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems

Arina A. Arkhipova (2003)

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

It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...

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