Riesz potential estimates for parabolic equations with measurable nonlinearities

Sun Sig Byun, Youchan Kim

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We study a nonlinear parabolic equation with measurable nonlinearity and measure data: ut-div a(Du,u, x, t) = μ in ωT . We obtain an optimal point-wise estimate for the gradient of a solution in terms of a certain Riesz potential of the right-hand measure in a very general setting that the nonlinearity is not only allowed to be measurable in one of spatial variables, but also depends on the variable of the possibly unbounded solution itself.

Original languageEnglish
Pages (from-to)6737-6779
Number of pages43
JournalInternational Mathematics Research Notices
Volume2018
Issue number21
DOIs
StatePublished - 5 Nov 2018

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