Layer and stable solutions to a nonlocal model

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)

Cites Work

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Nonlocal diffusion and applications
An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions
On De Giorgi's conjecture in dimension \(N\geq 9\)
Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
On a conjecture of De Giorgi and some related problems
On De Giorgi's conjecture in dimensions 4 and 5
The logarithmic tail of Néel walls
Rigidity of minimizers in nonlocal phase transitions
A three-dimensional symmetry result for a phase transition equation in the genuinely nonlocal regime
Harnack inequality for non-local Schrödinger operators
On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\)
Some energy estimates for stable solutions to fractional Allen-Cahn equations
Regularity of flat level sets in phase transitions
Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
Optimal grid-based methods for thin film micromagnetics simulations
2-D stability of the Néel wall
Sharp energy estimates for nonlinear fractional diffusion equations
The Liouville property and a conjecture of De Giorgi.
Improvement of Flatness for Nonlocal Phase Transitions
Regularity of the obstacle problem for a fractional power of the laplace operator
Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
Repulsive Interaction of Néel Walls, and the Internal Length Scale of the Cross-Tie Wall
One-dimensional magnetic domain walls
Rigidity of Minimizers in Nonlocal Phase Transitions II
Uniqueness of one-dimensional Néel wall profiles
An Extension Problem Related to the Fractional Laplacian
Wave-type dynamics in ferromagnetic thin films and the motion of Néel walls
Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
Layer solutions in a half‐space for boundary reactions
On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

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