Regularity for nonlinear equations involving square Hörmander operators

DOI10.1016/0362-546X(94)90251-8zbMath0868.47041OpenAlexW1975647002MaRDI QIDQ4312094

Ugo Gianazza

Publication date: 17 August 1997

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)90251-8

zbMATH Keywords

boundary value problemregularity propertiesCarathéodory functionCaccioppoli inequalityformal adjointsmoothness assumptionuniform Hörmander condition

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Second-order elliptic equations (35J15)

Related Items (11)

A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields ⋮ \(L^p\) estimates for weak solutions to nonlinear degenerate parabolic systems ⋮ \(W^{2,1+\varepsilon}\) estimates for the Monge-Ampère equation ⋮ Estimates in Morrey spaces and Hölder continuity for weak solutions to degenerate elliptic systems ⋮ Interior \(W_\ast^{1, p(x, t)}\)-regularity for parabolic divergence equations of Hörmander's type ⋮ Homogenization and Convergence of Correctors in Carnot Groups ⋮ Hölder regularity for weak solutions to divergence form degenerate quasilinear parabolic systems ⋮ Partial regularity for degenerate subelliptic systems associated with Hörmander's vector fields ⋮ Regularity in Orlicz spaces for non-divergence degenerate elliptic equations on homogeneous groups ⋮ Regularity for weak solutions to nondiagonal quasilinear degenerate elliptic systems ⋮ Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients

Cites Work

• Fundamental solutions and geometry of the sum of squares of vector fields
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
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