Abstract
We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-Laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic p-capacity.
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Acknowledgements
The authors thank Juha Kinnunen, who suggested this problem, during the program “Evolutionary problems” in the Fall 2013 at the Institut Mittag-Leffler, and are very grateful to Emmanuele DiBenedetto, for discussions and comments, which greatly helped to improve the final version of this manuscript. We thank the anonymous referee for his remarks.
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Dedicated to Emmanuele DiBenedetto for his 70th birthday.
Naian Liao is partially supported by NSFC 11701054 Grant.
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Gianazza, U., Liao, N. & Lukkari, T. A boundary estimate for singular parabolic diffusion equations. Nonlinear Differ. Equ. Appl. 25, 33 (2018). https://doi.org/10.1007/s00030-018-0523-9
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DOI: https://doi.org/10.1007/s00030-018-0523-9