Hessian inequalities and the fractional Laplacian

DOI10.1515/CRELLE.2011.116zbMath1273.49047OpenAlexW2077394054MaRDI QIDQ2898925

Igor E. Verbitsky, Fausto Ferrari, Bruno Franchi

Publication date: 12 July 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2011.116

zbMATH Keywords

fractional LaplacianHessian energy\(k\)-convex functionfractional Sobolev energy

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Miscellaneous topics in calculus of variations and optimal control (49N99) Fractional partial differential equations (35R11) Monge-Ampère equations (35J96)

Related Items (10)

Uniqueness for fractional parabolic and elliptic equations with drift ⋮ Radial fractional Laplace operators and Hessian inequalities ⋮ Biharmonic elliptic problems involving the 2nd Hessian operator ⋮ Steiner's formula in the Heisenberg group ⋮ Uniqueness in weighted Lebesgue spaces for a class of fractional parabolic and elliptic equations ⋮ Quasilinear and Hessian type equations with exponential reaction and measure data ⋮ Mean Hölder-Lipschitz potentials in curved Campanato-Radon spaces and equations \((-\Delta)^{\frac{\alpha}{2}}u=\mu = F_k[u\)] ⋮ The Hessian Sobolev inequality and its extensions ⋮ Regularity and capacity for the fractional dissipative operator ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations

Cites Work

• Unnamed Item
• Thin sets in nonlinear potential theory
• Potential estimates for a class of fully nonlinear elliptic equations.
• Weighted trace inequalities for fractional integrals and applications to semilinear equations
• Hessian measures. II
• Quasilinear and Hessian equations of Lane-Emden type
• Nonlinear equations and weighted norm inequalities
• An Extension Problem Related to the Fractional Laplacian

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