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math-ph2014★ 18 cited
Orbital-free density functional theory of out-of-plane charge screening in graphene
Jianfeng Lu, Vitaly Moroz, Cyrill B. Muratov
We propose a density functional theory of Thomas-Fermi-Dirac-von Weizsäcker type to describe the response of a single layer of graphene resting on a dielectric substrate to a point…
math.AP2014★ 217 cited
Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent
Vitaly Moroz, Jean Van Schaftingen
We consider nonlinear Choquard equation $$ - Δu + V u = \bigl(I_α\ast |u|^{\fracα{N}+1}\bigr) |u|^{\fracα{N}-1} u\quad\text{in (\mathbb{R}^N)},$$ where , $V \in L^\infty (…