– Europe/Lisbon
Room P1, Mathematics Building — Online

Lucio Boccardo, Università di Roma La Sapienza
Recent developments on Dirichlet problems with singular convection/drift terms
In the talk we discuss two Dirichlet problems ("formally" in duality)
In the first part we briefly recall some recent results:
- existence and summability properties of weak solutions (
), if ; - Calderon-Zygmund theory (
, infinite energy solutions), if ; - uniqueness;
- the case
, where ; - the case
.
Then we show:
- a new (simpler) existence proof, thanks to the presence of the zero order term, for
;(CP) - a straight duality proof for
;(DP) - continuous dependence of the solutions with respect to the weak convergence of the coefficients;
- regularizing effect of dominated coefficients (
or , ); - "weak" maximum principle: if
[ ] and, of course, not =0 a.e., then [ ] and the set where [ ] is zero has zero measure (at most).
Work in progress: obstacle problem; nonlinear principal part.
Open problem: "strong" maximum principle.
Projecto FCT UIDB/04459/2020.
Projecto FCT UIDB/04459/2020.