Asymptotic mean value formulas for parabolic nonlinear equations

• Pablo Blanc ^[1] ; Fernando Charro ^[2] ; Juan J. Manfredi ^[3] ; Julio D. Rossi ^[4]
  1. [1] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
  2. [2] Wayne State University

     Wayne State University

     City of Detroit, Estados Unidos

     
  3. [3] University of Pittsburgh

     University of Pittsburgh

     City of Pittsburgh, Estados Unidos

     
  4. [4] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 137-164
• Idioma: inglés
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• Resumen

  • In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Amp`ere equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games.