期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
卷 -, 期 -, 页码 -出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2022144
关键词
Mean value formulas; degenerate elliptic operators; Carnot groups
资金
- Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)
- INFN, Seione di Lecce
- Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)
This paper proves surface and volume mean value formulas for classical solutions to uniformly elliptic equations with Holder continuous coefficients. It extends the formulas to subelliptic operators on Carnot groups, relying on the theory of finite perimeter sets on stratified Lie groups.
We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Holder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relative the adjoint differential operator. We then extend the aforementioned formulas to some subelliptic operators on Carnot groups. In this case we rely on the theory of finite perimeter sets on stratified Lie groups.
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