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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

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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