Boundary estimates for certain degenerate and singular parabolic equations

Avelin, Benny, Gianazza, Ugo, and Salsa, Sandro. "Boundary estimates for certain degenerate and singular parabolic equations." Journal of the European Mathematical Society 018.2 (2016): 381-424. <http://eudml.org/doc/277660>.

@article{Avelin2016,
abstract = {We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic $p$-Laplacian 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.},
author = {Avelin, Benny, Gianazza, Ugo, Salsa, Sandro},
journal = {Journal of the European Mathematical Society},
keywords = {degenerate and singular parabolic equations; Harnack estimates; boundary Harnack inequality; Carleson estimate; degenerate and singular parabolic equations; Harnack estimates; boundary Harnack inequality; Carleson estimate},
language = {eng},
number = {2},
pages = {381-424},
publisher = {European Mathematical Society Publishing House},
title = {Boundary estimates for certain degenerate and singular parabolic equations},
url = {http://eudml.org/doc/277660},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Avelin, Benny
AU - Gianazza, Ugo
AU - Salsa, Sandro
TI - Boundary estimates for certain degenerate and singular parabolic equations
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 2
SP - 381
EP - 424
AB - We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic $p$-Laplacian 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.
LA - eng
KW - degenerate and singular parabolic equations; Harnack estimates; boundary Harnack inequality; Carleson estimate; degenerate and singular parabolic equations; Harnack estimates; boundary Harnack inequality; Carleson estimate
UR - http://eudml.org/doc/277660
ER -