On some properties of weak solutions to elliptic equations with divergence-free drifts

DOI10.1090/conm/710/14366zbMath1401.35101arXiv1707.03197OpenAlexW2963629437MaRDI QIDQ4686828

Nikolay Filonov, Timofey Shilkin

Publication date: 10 October 2018

Published in: Mathematical Analysis in Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.03197

zbMATH Keywords

Dirichlet problemelliptic equationsregularity of solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Quasilinear elliptic equations (35J62)

Related Items (7)

Scalar elliptic equations with a singular drift ⋮ The normal derivative lemma and surrounding issues ⋮ Elliptic equations in divergence form with drifts in 𝐿² ⋮ Dirichlet and Neumann problems for elliptic equations with singular drifts on Lipschitz domains ⋮ Regularity properties of passive scalars with rough divergence-free drifts ⋮ On some properties of weak solutions to elliptic equations with divergence-free drifts ⋮ Existence, Uniqueness, and Regularity Results for Elliptic Equations with Drift Terms in Critical Weak Spaces

Cites Work

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• Hölder continuity for a drift-diffusion equation with pressure
• On divergence-free drifts
• On the regularity of solutions to the equation \(-\Delta u+b\cdot\nabla u=0\)
• A strong regularity result for parabolic equations
• Extra regularity for parabolic equations with drift terms
• On the loss of continuity for super-critical drift-diffusion equations
• Regularity theorems for parabolic equations
• Remarks on the uniqueness of a solution of the Dirichlet problem for second-order elliptic equations with lower-order terms
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Linear and quasilinear elliptic equations
• The Harnack inequality and related properties for solutions of elliptic and parabolic equations with divergence-free lower-order coefficients
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• On some properties of weak solutions to elliptic equations with divergence-free drifts
• Form boundedness of the general second‐order differential Operator

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