RESEARCH ARTICLE
Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions
Alessandro Goffi,
Corresponding Author
Alessandro Goffi
Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy
Correspondence
Alessandro Goffi, Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, via Trieste 63, 35121 Padua, Italy.
Email: [email protected]
Search for more papers by this authorAlessandro Goffi,
Corresponding Author
Alessandro Goffi
Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Padua, Italy
Correspondence
Alessandro Goffi, Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, via Trieste 63, 35121 Padua, Italy.
Email: [email protected]
Search for more papers by this authorFirst published: 17 February 2024
Abstract
In this note, we prove interior a priori first- and second-order estimates for solutions of fully nonlinear degenerate elliptic inequalities structured over the vector fields of Carnot groups, under the main assumption that is semiconvex along the fields. These estimates for supersolutions are new even for linear subelliptic inequalities in nondivergence form, whereas in the nonlinear setting they do not require neither convexity nor concavity on the second derivatives. We complement the analysis exhibiting an explicit example showing that horizontal regularity of Calderón–Zygmund type for fully nonlinear subelliptic equations posed on the Heisenberg group cannot be in general expected in the range , being the homogeneous dimension of the group.
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