Maximum principle for non-uniformly parabolic equations and applications

• Autores: Xicheng Zhang
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 25, Nº 3, 2024, págs. 1267-1308
• Idioma: inglés
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• Resumen

  • In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi’s iteration.

    As applications, we show the existence of weak solutions for possibly degener- ate stochastic differential equations with singular diffusion and drift coefficients.

    Moreover, by the Markov selection theorem of Krylov [8], we also establish the existence of the associated strong Markov family.