On the optimality of the assumptions used to prove the existence and symmetry of minimizers of some fractional constrained variational problems

DOI10.1007/s00023-012-0212-xzbMath1267.49018OpenAlexW1970116373MaRDI QIDQ2377318

Hichem Hajaiej

Publication date: 28 June 2013

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00023-012-0212-x

zbMATH Keywords

fractional constrained variational problemsradial minimizersradially decreasing minimizers

Mathematics Subject Classification ID

Variational principles of physics (49S05) Existence theories in calculus of variations and optimal control (49J99)

Related Items (15)

On the optimality of the assumptions used to prove the existence and symmetry of minimizers of some fractional constrained variational problems ⋮ Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians ⋮ Existence of minimizers of functionals involving the fractional gradient in the absence of compactness, symmetry and monotonicity ⋮ Minimizers of fractional NLS energy functionals in \(\mathbb{R}^2\) ⋮ Existence results for a critical fractional equation ⋮ Unnamed Item ⋮ Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in \(\mathbb{R}^{N}\) ⋮ Multiplicity and concentration of solutions for a fractional Kirchhoff equation with magnetic field and critical growth ⋮ A multiplicity results for a singular problem involving the fractionalp-Laplacian operator ⋮ On a fractional Schrödinger equation in the presence of harmonic potential ⋮ Symmetry of minimizers of some fractional problems ⋮ On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians ⋮ A sharp Gagliardo-Nirenberg inequality and its application to fractional problems with inhomogeneous nonlinearity ⋮ Sharp embedding of Sobolev spaces involving general kernels and its application ⋮ On a New Class of Variational Problems

Cites Work

• Unnamed Item
• Existence of solitary waves in higher dimensions
• Existence of minimizers of functionals involving the fractional gradient in the absence of compactness, symmetry and monotonicity
• Fractional calculus for power functions and eigenvalues of the fractional Laplacian
• On the optimality of the assumptions used to prove the existence and symmetry of minimizers of some fractional constrained variational problems
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates

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