Hölder estimate for a tug-of-war game with 1 < p < 2 from Krylov–Safonov regularity theory

• Ángel Arroyo ^[1] ; Mikko Parviainen ^[2]
  1. [1] Universitat d'Alacant

     Universitat d'Alacant

     Alicante, España

     
  2. [2] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 1023-1044
• Idioma: inglés
• DOI: 10.4171/RMI/1462
• Enlaces
  • Texto completo
• Resumen

  • We propose a new version of the tug-of-war game and a corresponding dynamic programming principle related to the p-Laplacian with 1 < p < 2. For this version, the asymptotic Hölder continuity of solutions can be directly derived from recent Krylov–Safonov type regularity results in the singular case. Moreover, existence of a measurable solution can be obtained without using boundary corrections. We also establish a comparison principle.