Parabolic equations with BMO nonlinearity in Reifenberg domains

DOI10.1515/CRELLE.2008.007zbMath1160.35035MaRDI QIDQ5459230

Lihe Wang, Sun-Sig Byun

Publication date: 25 April 2008

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

zbMATH Keywords

divergence formfractal boundariesglobal \(L^p\)-estimate of the gradient

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) PDEs with low regular coefficients and/or low regular data (35R05)

Related Items (17)

Lorentz estimates for degenerate and singular evolutionary systems ⋮ Gradient weighted norm inequalities for very weak solutions of linear parabolic equations with BMO coefficients ⋮ Global weighted estimates for the nonlinear parabolic equations with non-standard growth ⋮ Global gradient estimates for parabolic equations with measurable nonlinearities ⋮ Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains ⋮ Potential Estimates and Quasilinear Parabolic Equations with Measure Data ⋮ Gradient estimates for parabolic \(\mathcal A\)-harmonic equations ⋮ Global Calderón-Zygmund theory for parabolic \(p\)-Laplacian system: the case \(1 < p \leq \frac{ 2 n}{ n + 2} \) ⋮ Universal potential estimates ⋮ Lorentz estimates for obstacle parabolic problems ⋮ New perturbation methods for nonlinear parabolic problems ⋮ Global gradient estimates for the parabolic \(p(x, t)\)-Laplacian equation ⋮ Global Calderón-Zygmund theory for nonlinear parabolic systems ⋮ Singular parabolic equations, measures satisfying density conditions, and gradient integrability ⋮ Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data ⋮ Lorentz Estimates for Weak Solutions of Quasi-linear Parabolic Equations with Singular Divergence-free Drifts ⋮ Estimates for parabolic equations with measure data in generalized Morrey spaces

Cites Work

• Interior a priori estimates for solutions of fully nonlinear equations
• Traces of Sobolev functions on fractal type sets and characterization of extension domains
• Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• On \(BMO\) regularity for linear elliptic systems
• Parabolic equations in Reifenberg domains
• Free boundary regularity for harmonic measures and Poisson kernels
• Higher integrability for parabolic systems of \(p\)-Laplacian type
• On functions of bounded mean oscillation
• Elliptic systems of PDE with BMO-coefficients

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