Boundary Estimates for Certain Degenerate and Singular Parabolic Equations
2016 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 18, no 2, 381-424 p.Article in journal (Refereed) Published
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic p-Laplace equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part S-T of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular parabolic equations of porous medium type.
Place, publisher, year, edition, pages
2016. Vol. 18, no 2, 381-424 p.
Degenerate and singular parabolic equations; Harnack estimates; boundary Harnack inequality; Carleson estimate
IdentifiersURN: urn:nbn:se:uu:diva-186267DOI: 10.4171/JEMS/593ISI: 000370249100005OAI: oai:DiVA.org:uu-186267DiVA: diva2:572812