A boundary estimate for singular parabolic diffusion equations

  • Ugo Gianazza
  • Naian Liao
  • Teemu Lukkari


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.


Parabolic p-Laplacian Boundary estimates Continuity Elliptic p-capacity Wiener-type integral 

Mathematics Subject Classification

Primary 35K67 35B65 Secondary 35B45 35K20 



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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Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Casorati”Università di PaviaPaviaItaly
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingChina
  3. 3.Department of MathematicsAalto UniversityEspooFinland

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