Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups

DOI10.3934/DCDSS.2022144arXiv2204.11541OpenAlexW4289826875WikidataQ113692660 ScholiaQ113692660MaRDI QIDQ6397386

Sergio Polidoro, Diego Pallara

Publication date: 25 April 2022

Abstract: We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with H"{o}lder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relevant 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 perimeters on stratified Lie groups.

Full work available at URL: https://doi.org/10.3934/dcdss.2022144

Mathematics Subject Classification ID

Operator theory (47-XX) Elliptic equations and elliptic systems (35Jxx)

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