On Weak Solutions of Elliptic Equations with Singular Drifts

DOI10.1137/14096270XzbMath1317.35028OpenAlexW2040879194MaRDI QIDQ5253459

Young-Heon Kim, Hyun-Seok Kim

Publication date: 26 May 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/14096270x

zbMATH Keywords

weak solutionselliptic equationssingular drift terms

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Second-order elliptic equations (35J15) Weak solutions to PDEs (35D30)

Related Items (14)

Scalar elliptic equations with a singular drift ⋮ Noncoercive quasilinear elliptic operators with singular lower order terms ⋮ Existence and uniqueness of weak solution in \(W^{1,2+ \epsilon }\) for elliptic equations with drifts in weak-\(L^n\) spaces ⋮ Elliptic equations in divergence form with drifts in 𝐿² ⋮ Dirichlet and Neumann problems for elliptic equations with singular drifts on Lipschitz domains ⋮ Stampacchia–Caldéron–Zygmund theory for linear elliptic equations with discontinuous coefficients and singular drift ⋮ Dirichlet problems for second order linear elliptic equations with \(L^1 \)-data ⋮ On \(L^p\)-resolvent estimates for second-order elliptic equations in divergence form ⋮ Weak solutions for the Oseen system in 2D and when the given velocity is not sufficiently regular ⋮ An optimal control problem for some nonlinear elliptic equations with unbounded coefficients ⋮ \(W^{1,p}\)-estimates for elliptic equations with lower order terms ⋮ Existence, Uniqueness, and Regularity Results for Elliptic Equations with Drift Terms in Critical Weak Spaces ⋮ Quasilinear elliptic equations with natural growth and quasilinear elliptic equations with singular drift ⋮ Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms

Cites Work

• Unnamed Item
• Unnamed Item
• The Harnack inequality for second-order elliptic equations with divergence-free drifts
• On divergence-free drifts
• Existence and uniqueness for nonlinear elliptic equations with lower-order terms
• Stationary Stokes, Oseen and Navier-Stokes equations with singular data
• On the regularity of solutions to the equation \(-\Delta u+b\cdot\nabla u=0\)
• Existence and regularity of very weak solutions of the stationary Navier-Stokes equations
• Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms
• Elliptic equations in divergence form with partially BMO coefficients
• Stationary solutions to the Navier-Stokes equations in dimension four
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• Elliptic partial differential equations of second order
• Non-coercive linear elliptic problems
• Compensated compactness and Hardy spaces
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Existence and uniqueness for elliptic equations with lower-order terms
• Dirichlet Problem for the Stationary Navier-Stokes System on Lipschitz Domains
• The Harnack inequality and related properties for solutions of elliptic and parabolic equations with divergence-free lower-order coefficients
• Global and Local Estimates for Nonlinear Noncoercive Elliptic Equations with Measure Data

This page was built for publication: On Weak Solutions of Elliptic Equations with Singular Drifts