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Existence of groundstates for a class of nonlinear Choquard equations
Vitaly Moroz, Jean Van Schaftingen
We prove the existence of a nontrivial solution (u \in H^1 (\R^N)) to the nonlinear Choquard equation [- Δu + u = \bigl(I_α\ast F (u)\bigr) F' (u) \quad \text{in (\R^N),}] where (I…
Density of smooth maps for fractional Sobolev spaces into simply connected manifolds when
Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen
Given a compact manifold , and , we prove that the class of smooth maps on the cube with values into is strongly dense i…
Nonlocal Hardy type inequalities with optimal constants and remainder terms
Vitaly Moroz, Jean Van Schaftingen
Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{φ(x)}{\abs{x}^\fracα{2}} I_α(x - y) \frac{φ(y…
Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
Vitaly Moroz, Jean Van Schaftingen
We consider a semilinear elliptic problem [- Δu + u = (I_α\ast \abs{u}^p) \abs{u}^{p - 2} u \quad\text{in (\mathbb{R}^N),}] where (I_α) is a Riesz potential and (p>1). This family…
Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
Vitaly Moroz, Jean Van Schaftingen
We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard o…
Strong density for higher order Sobolev spaces into compact manifolds
Pierre Bousquet, Augusto Ponce, Jean Van Schaftingen
Given a compact manifold , an integer and an exponent , we prove that the class of smooth maps on the cu…