Maximizers for Gagliardo–Nirenberg inequalities and related non-local problems

2014/05/08 by Jacopo Bellazzini, Rupert L. Frank, Nicola Visciglia · 10 citations
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · doi:10.1007/s00208-014-1046-2

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics
• Nonlinear Schr�dinger equations and sharp interpolation estimates
• Existence of solitary waves in higher dimensions
• A relation between pointwise convergence of functions and convergence of functionals

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• Symmetry breaking for Schrödinger-Poisson-Slater energy
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• Discrete Caffarelli-Kohn-Nirenberg inequalities and ground state solutions to nonlinear elliptic equations
• Instability of algebraic standing waves for nonlinear Schr''odinger equations with triple power nonlinearities
• Some remarks on a minimization problem associated to a fourth order nonlinear Schrödinger equation
• An Improvement on the Brézis-Gallouët technique for 2D NLS and 1D half-wave equation
• Sharp constants and optimizers for a class of the Caffarelli-Kohn-Nirenberg inequalities