# Boundary estimates for certain degenerate and singular parabolic equations

Benny Avelin; Ugo Gianazza; Sandro Salsa

Journal of the European Mathematical Society (2016)

- Volume: 018, Issue: 2, page 381-424
- ISSN: 1435-9855

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topAvelin, 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 -

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