15:00 – Zeev Sobol (Swansea): Estimates of solutions to degenerate quasi-linear parabolic equations via parabolic analogs of Wolff potentials.
Abstract: The talk will introduce a parabolic analog of Wolff potential used to derive pointwise estimates of solutions to degenerate quasi-linear parabolic equations with measures in the right hand side. The result generalises the celebrated Kilpelainen-Maly result for parabolic equations.
16:30 – Sergey Mikhailov (Brunel): Generalized Co-normal Derivatives and Boundary Value Problems for Elliptic PDEs.
Abstract: Elliptic PDE systems of the second order on a Lipschitz domain are considered in the talk. For functions from the Sobolev space Hs(Ω), 1/2 < s < 3/2 , a defnition of non- unique generalized co-normal derivative is given, which is related to possible non-unique extensions of a partial differential operator and PDE right hand side from the domain to its boundary. For a (rather wide) subspace of Hs(Ω), the unique canonical co-normal derivative is also defined and it is proved that the canonical co-normal derivative coincides with the classical one when the both exist. A generalization of the boundary value problem variational settings, which makes them insensitive to the co-normal derivative inherent non-uniqueness is also discussed.
The talk is related to papers [1, 2].
References
[1] S. E. Mikhailov. Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains. J. Math. Analysis and Appl., 378, 324{342, 2011.
[2] S. E. Mikhailov. Solution regularity and co-normal derivatives for elliptic systems with non-smooth coe_cients on Lipschitz domains, (submitted for publication).