On the impossibility of \(W_p^2\) estimates for elliptic equations with piecewise constant coefficients

DOI10.1016/j.jfa.2014.09.013zbMath1302.35143arXiv1404.5647OpenAlexW2963741855WikidataQ60138092 ScholiaQ60138092MaRDI QIDQ461719

Hongjie Dong, Do-Yoon Kim

Publication date: 13 October 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.5647

zbMATH Keywords

counterexamples\(W_p^2\) estimateselliptic equations with piecewise constant coefficients

Mathematics Subject Classification ID

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 (6)

Sharp Hessian integrability estimates for nonlinear elliptic equations: an asymptotic approach ⋮ On parabolic equations in one space dimension ⋮ Sharp Hessian estimates for fully nonlinear elliptic equations under relaxed convexity assumptions, oblique boundary conditions and applications ⋮ Weighted \(L_{q}\)-estimates for stationary Stokes system with partially BMO coefficients ⋮ An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates ⋮ Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms

Cites Work

• On elliptic equations in a half space or in convex wedges with irregular coefficients
• Second order elliptic equations in \(\mathbb{R}^{d}\) with piecewise continuous coefficients
• Uniqueness for diffusions with piecewise constant coefficients
• Sopra una classe di equazioni ellittiche a coefficienti misurabili
• Parabolic Equations in Simple Convex Polytopes with Time Irregular Coefficients
• Second-order elliptic and parabolic equations with $B(\mathbb{R}^{2}, VMO)$ coefficients
• Elliptic Differential Equations with Coefficients Measurable with Respect to One Variable and VMO with Respect to the Others
• On elliptic equations with piecewise constant coefficients
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the impossibility of \(W_p^2\) estimates for elliptic equations with piecewise constant coefficients