On Mean Value formulas for solutions to second order linear PDEs

• Giovanni Cupini ^[1] ; Ermanno Lanconelli ^[1]
  1. [1] University of Bologna

     University of Bologna

     Bolonia, Italia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 2, 2021, págs. 777-809
• Idioma: inglés
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• Resumen

  • In this paper we give a general proof of Mean Value formulas for solutions to second order linear PDEs, only based on the local properties of their fundamental solution 0. Our proof requires a kind of pointwise vanishing integral condition for the intrinsic gradient of 0. Combining our Mean Value formulas with a “descent method” due to Kuptsov, we obtain formulas with improved ker- nels. As an application, we implement our general results to heat operators on stratified Lie groups and to Kolmogorov operators