Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients

Key Points

Solutions exist for nonlinear elliptic equations with measurable coefficients and zero Dirichlet boundary condition, indicating a strong potential impact.
The main term derives from a nonlinear operator associated with vector fields satisfying Poincaré inequality; notable properties emerge.
Demonstrated is a generalization of the L^p regularity results, extending concepts applied to Leray–Lions type equations.
Implications may enable further exploration of nonlinear behaviors in elliptic equations, enhancing understanding in mathematical analysis.

Abstract

We prove an existence result for solutions to a class of nonlinear degenerate elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form associated to a family of vector fields which satisfy a Poincaré inequality and the doubling condition. Furthermore, we prove that the solutions satisfy a generalization of the Lᵖ -regularity results which hold for the solutions to Leray–Lions type equations.

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Authors

Marco Picerni

Journals

Annali di Matematica Pura ed Applicata (1923 -)

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Institutions

Scuola Internazionale Superiore di Studi Avanzati

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Marco Picerni (Sat,) studied this question.

synapsesocial.com/papers/69a76104c6e9836116a2e81d — DOI: https://doi.org/10.1007/s10231-026-01667-3

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Existence and regularity results for p-Laplacian boundary value problems· 2014 · 4 citations
Elliptic Partial Differential Equations· 2013 · 136 citations
A characterization of pseudo-monotone differential operators in divergence form.<sup>†</sup>· 1984 · 8 citations
Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups· 2022 · 5 citations
Gradient regularity for elliptic equations in the Heisenberg group· 2009 · 92 citations

Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients

Key Points

Abstract

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Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study

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Also consider