PDE Real Analysis Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2017/11/15

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Kaj Nyström (Uppsala University)
Boundary value problems for parabolic equations with measurable coefficients (English)
[ Abstract ]
In recent joint works with P. Auscher and M. Egert we establish new results concerning boundary value problems in the upper half-space for second order parabolic equations (and systems) assuming only measurability and some transversal regularity in the coefficients of the elliptic part. To establish our results we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green's representation for solutions in natural classes involving square functions and non-tangential maximal functions, well-posedness results with data in $L^2$-Sobolev spaces together with invertibility of layer potentials, and perturbation results. In addition we solve the Kato square root problem for parabolic operators with coefficients of the elliptic part depending measurably on all variables. Using these results we are also able to solve the $L^p$-Dirichlet problem for parabolic equations with real, time-dependent, elliptic but non-symmetric coefficients. In this talk I will briefly describe some of these developments.