A note on the maximum principle for second-order elliptic equations in general domains

DOI10.1007/s10114-007-0976-yzbMath1137.35323OpenAlexW2163499687MaRDI QIDQ2477791

Antonio Vitolo

Publication date: 14 March 2008

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-007-0976-y

zbMATH Keywords

maximum principleelliptic equationsABP estimatenon-divergence form operatorsboundary weak Harnack inequality

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Second-order elliptic equations (35J15)

Related Items (9)

Maximum principle in some unbounded domains for an elliptic operator with unbounded drift ⋮ Singular elliptic equations with directional diffusion ⋮ Maximum principles for Laplacian and fractional Laplacian with critical integrability ⋮ Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains ⋮ Maximum principles for viscosity solutions of weakly elliptic equations ⋮ On bounds for steady waves with negative vorticity ⋮ Nonexistence of subcritical solitary waves ⋮ On the amplitude and the flow force constant of steady water waves ⋮ Regularity properties for a class of non-uniformly elliptic Isaacs operators

Cites Work

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• Some results on subelliptic equations
• On the maximum principle for complete second-order elliptic operators in general domains.
• On the maximum principle for second-order elliptic operators in unbounded domains
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• On the alexandroff‐bakelman‐pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations
• Dirichlet problems for the quasilinear second order subelliptic equations

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