On the Schauder estimates of solutions to parabolic equations

• Qing Han ^[1]
  1. [1] University of Notre Dame

     University of Notre Dame

     Township of Portage, Estados Unidos

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 27, Nº 1, 1998, págs. 1-26
• Idioma: inglés
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• Resumen

  • In this paper we give a priori estimates on asymptotic polynomials of solutions to parabolic differential equations at any points. This leads to a pointwise version of Schauder estimates. The result in this paper improves the classical Schauder estimates in a way that the estimates of solutions and their derivatives at one point depend on the coefficient and nonhomogeneous terms at this particular point.