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math.AP2013★ 179 cited
Limiting Bourgain-Brezis estimates for systems: theme and variations
Jean Van Schaftingen
J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case of sin…
math.AP2013★ 4 cited
Gelfand type problem for two phase porous media
Peter V. Gordon, Vitaly Moroz
We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to t…
math.AP2013★ 179 cited
Semi-classical states for the Choquard equation
Vital Moroz, Jean Van Schaftingen
We study the nonlocal equation $$-\varepsilon^2 Δu_\varepsilon + V u_\varepsilon = \varepsilon^{-α} \bigl(I_α\ast \lvert u_\varepsilon\rvert^p\bigr) \lvert u_\varepsilon \rvert^{p…