Elliptic second order equations

DOI10.1007/BF02925245zbMath0726.35036MaRDI QIDQ3349986

Luis A. Caffarelli

Publication date: 1988

Published in: Rendiconti del Seminario Matematico e Fisico di Milano (Search for Journal in Brave)

zbMATH Keywords

Harnack inequalityHölder regularityviscosity solutionsnon-divergence formCalderon- Zygmund \(L^ p\) estimates

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) PDEs with low regular coefficients and/or low regular data (35R05) Second-order elliptic equations (35J15)

Related Items (36)

Fractional elliptic equations, Caccioppoli estimates and regularity ⋮ Sublinear operators with rough kernel generated by Calderón-Zygmund operators and their commutators on generalized Morrey spaces ⋮ Variation inequalities related to Schrödinger operators on Morrey spaces ⋮ Smoothness of the intensity measure density for interacting branching diffusions with immigra\-tions ⋮ Two-type estimates for the boundedness of generalized Riesz potential operator in the generalized weighted local Morrey spaces ⋮ An application of global gradient estimates in Lorentz-Morrey spaces: The existence of stationary solution to degenerate diffusive Hamilton-Jacobi equations ⋮ Gradient estimates below the duality exponent ⋮ Boundary Lipschitz regularity of solutions for general semilinear elliptic equations in divergence form ⋮ Bounds for multilinear operators under an integral type condition on Morrey spaces ⋮ Discrete ABP estimate and convergence rates for linear elliptic equations in non-divergence form ⋮ CAUCHY–DIRICHLET PROBLEM ASSOCIATED TO DIVERGENCE FORM PARABOLIC EQUATIONS ⋮ Riesz potential in generalized Morrey spaces on the Heisenberg group ⋮ Regularity for \(C^{1, \alpha}\) interface transmission problems ⋮ Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces ⋮ The normal derivative lemma and surrounding issues ⋮ Elliptic equations with discontinuous coefficients in generalized Morrey spaces ⋮ Unnamed Item ⋮ Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains ⋮ The A. D. Aleksandrov maximum principle ⋮ \(L^p\)-estimates for the Hessians of solutions to fully nonlinear parabolic equations with oblique boundary conditions ⋮ Mixed Morrey spaces and their applications to partial differential equations ⋮ Unnamed Item ⋮ Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces ⋮ Borderline Estimates for Fully Nonlinear Elliptic Equations ⋮ Fully nonlinear elliptic equations and the dini condition ⋮ Some embeddings into the Morrey and modified Morrey spaces associated with the Dunkl operator ⋮ Hölder regularity for non-divergence-form elliptic equations with discontinuous coefficients ⋮ Schauder estimates for elliptic operators with applications to nodal sets. ⋮ Variation inequalities related to Schrödinger operators on weighted Morrey spaces ⋮ Boundedness of homogeneous fractional integral operator on Morrey space ⋮ Sharp integral estimates for the fractional maximal function and interpolation ⋮ An extension of the Muckenhoupt-Wheeden theorem to generalized weighted Morrey spaces ⋮ Compactness of commutators of Riesz potential on Morrey spaces ⋮ Taylor formula for homogeneous groups and applications ⋮ Global Morrey regularity of strong solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients ⋮ Boundedness and compactness for the commutators of bilinear operators on Morrey spaces

Cites Work

• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Limitazioni per soluzioni di equazioni ellittiche

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