Seminario del Prof V. Maz'ya mercoledì 7 Maggio 2014 alle 14 in aula 1B1.
Titolo: Differentiability of solutions to elliptic equations with non-Dini coefficients
Abstract: This is a survey of results on the conditions imposed on the coeffcients of 2nd order elliptic equations in divergence form, milder than the Dini-continuity, under which solutions must be Lipschitz continuous, or
even differentiable, at a given point, as well as some related topics.
Seminario della Prof T. Shaposhnikova mercoledì 7 Maggio 2014 alle 15 in aula 1B1
Titolo:Theory of Sobolev multipliers and their applications to differential and integral operators
Abstract: The talk is a survey of the theory of pointwise multipliers in
spaces of differentiable functions which was developed
together with V.Maz'ya. In particular, we discuss explicit
characterizations of multipliers in pairs of Sobolev spaces,
Bessel potential spaces, and Besov spaces. Sharp results
on essential norms and compactness properties of the
multipliers, as well as trace, extension and composition theorems for
the multipliers are presented.
We also give various applications of our theory to differential
and integral operators, addressing such topics as regularity
of the boundary for elliptic boundary value problems and
continuity of general differential operators in pairs of Sobolev