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Pointwise estimates of solutions to parabolic equations in terms of the parabolic potentials
Mon 18 February 2013, 16:00
Olena Sivak
University of Swansea
Organiser: Michiel van den Berg
ABSTRACT
We consider a class of quasilinear parabolic equations in divergence form modeled by the evolutionary p-Laplacean with a spatial degeneracy with a measure in the right hand side. We prove pointwise estimates for solutions to these equations in terms of the truncated non-linear parabolic potential of the measure. This is an extension of pointwise estimates for p-Laplace type elliptic equations in terms of the nonlinear Wolff potential obtained by T. Kilpeläinen and J. Malý (1994). This is joint work with Vitali Liskevich (Swansea University, UK) and Zeev Sobol (Swansea University, UK)