Variational problems with long-range interaction

DOI10.1007/s00205-017-1204-2zbMath1394.35520arXiv1701.05005OpenAlexW2580802007MaRDI QIDQ1750302

Alessandro Zilio, Nicola Soave, Hugo Tavares, Susanna Terracini

Publication date: 18 May 2018

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.05005

zbMATH Keywords

variational problemminimizationfree boundary conditionsrepelling inerations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Variational methods applied to PDEs (35A15) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Optimization of shapes other than minimal surfaces (49Q10) Free boundary problems for PDEs (35R35) Weak solutions to PDEs (35D30)

Related Items (5)

Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius ⋮ Global minimizers of coexistence for strongly competing systems involving the square root of the Laplacian ⋮ An anisotropic monotonicity formula, with applications to some segregation problems ⋮ Gradient regularity in mixed local and nonlocal problems ⋮ Regularity results for segregated configurations involving fractional Laplacian

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extremality conditions and regularity of solutions to optimal partition problems involving Laplacian eigenvalues
• Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping
• Sign-changing solutions of competition-diffusion elliptic systems and optimal partition problems
• Minimal partitions and image classification using a gradient-free perimeter approximation
• Uniform bounds for strongly competing systems: the optimal Lipschitz case
• Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian
• On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects
• The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture
• Regularity of the nodal set of segregated critical configurations under a weak reflection law
• Functional analysis, Sobolev spaces and partial differential equations
• Functionals defined on partitions in sets of finite perimeter. I: Integral representation and Gamma-convergence
• Elliptic partial differential equations of second order
• On a long range segregation model
• Uniqueness result for long range spatially segregation elliptic system
• On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae
• Nehari's problem and competing species systems.
• An optimal partition problem related to nonlinear eigenvalues.
• Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates
• Uniform Hölder regularity with small exponent in competition-fractional diffusion systems
• Asymptotic estimates for the spatial segregation of competitive systems
• Variation and optimization of formes. A geometric analysis
• An optimal partition problem for eigenvalues
• Strong Competition versus Fractional Diffusion: The Case of Lotka-Volterra Interaction
• Optimal Partitions for Eigenvalues
• Curvature Measures
• Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition
• Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
• Mathematical issues in the modelling of supersolids
• A variational problem for the spatial segregation of reaction-diffusion systems
• Asymptotic behaviour of solutions of planar elliptic systems with strong competition

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