Ground states of semilinear elliptic problems with applications to the Allen-Cahn equation on the sphere
From MaRDI portal
Publication:2113325
DOI10.1007/s00526-021-02106-2zbMath1492.35113OpenAlexW4211235870WikidataQ114018080 ScholiaQ114018080MaRDI QIDQ2113325
Henrik Matthiesen, Rayssa Caju, Marco A. M. Guaraco, Pedro Gaspar
Publication date: 14 March 2022
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-021-02106-2
Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)
Related Items (3)
Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere ⋮ The p-widths of a surface ⋮ Symmetric mean curvature flow on the \(n\)-sphere
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in \(\mathbb{R}^3\)
- Stable solutions of elliptic equations on Riemannian manifolds
- Symmetry of solutions to variational problems for nonlinear elliptic equations via reflection methods
- Nonlinear scalar field equations. I: Existence of a ground state
- Explicit approximation of the symmetric rearrangement by polarizations
- On a semilinear diffusion equation on a Riemannian manifold and its stable equilibrium solutions
- Maximum principles and their applications
- Instability results for reaction-diffusion equations with Neumann boundary conditions
- A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator
- The Allen-Cahn equation on closed manifolds
- From constant mean curvature hypersurfaces to the gradient theory of phase transitions.
- A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature
- Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
- Remarks on 4-dimensional differentiable manifolds
- Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
- Symmetry of solutions of semilinear elliptic problems
- Min-max theory and the Willmore conjecture
- Steiner symmetric extremals in Pólya-Szegő-type inequalities
- Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems
- Minimal Surfaces with Low Index in the Three-Dimensional Sphere
- Symmetrization in Analysis
- Symmetry of solutions to semilinear elliptic equations via Morse index
- Remarks on sublinear elliptic equations
- Morse index of some min-max critical points. I. Application to multiplicity results
- Symmetric Decreasing Rearrangement Is Sometimes Continuous
- A Note on a Mountain Pass Characterization of Least Energy Solutions
- A remark on least energy solutions in $\mathbf {R}^N$
- Convergence of the Allen--Cahn Equation with Neumann Boundary Conditions
- Symmetry of nodal solutions for singularly perturbed elliptic problems on a ball
This page was built for publication: Ground states of semilinear elliptic problems with applications to the Allen-Cahn equation on the sphere