Technion - Israel Institute of Technology
Department of Mathematics
DATE: Tuesday, March 1, 2011
SPEAKER: Professor Vitali Liskevich, Swansea Univesity ,UK
TITLE: Pointwise and gradient estimates for a class of quasi-linear
       parabolic equations
PLACE: Room 814, Amado Mathematics Building, Technion
TIME: 14:30
.In this talk we will discuss basic regularity properties of second
order quasi-linear elliptic and parabolic
equation of divergence type. First we present pointwise estimates for
solutions of evolutional p-Laplace
equations and porous media equations with measure as a forcing term.
Next, for the general structure of
the quasi-linear elliptic and parabolic equations with lower order
terms we establish optimal conditions for
local boundedness of solutions, continuity and the validity of the
Harnack inequality. Finally, assuming the
the divergence structure of the main part of the p-Laplace type
evolution equation is differentiable, we will
present the estimates for the gradients of solutions and establish
sufficient conditions for Lipschitz continuity.
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