A New Proof for the Existence of an Equivariant Entire Solution Connecting the Minima of the Potential for the System Δu − Wu(u) = 0
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Publication:4902760
DOI10.1080/03605302.2012.721851zbMath1268.35051arXiv1106.0919OpenAlexW2023052108MaRDI QIDQ4902760
Publication date: 17 January 2013
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1106.0919
Related Items (10)
On the heteroclinic connection problem for multi-well gradient systems ⋮ Entire minimizers of Allen-Cahn systems with sub-quadratic potentials ⋮ Unnamed Item ⋮ Equivariant entire solutions to the elliptic system \(\Delta u = W_u(u)\) for general \(G\)-invariant potentials ⋮ Metric methods for heteroclinic connections in infinite dimensional spaces ⋮ A maximum principle for systems with variational structure and an application to standing waves ⋮ Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures ⋮ A tale of two approaches to heteroclinic solutions for Φ-Laplacian systems ⋮ On the loss of compactness in the vectorial heteroclinic connection problem ⋮ Density estimates for vector minimizers and applications
Cites Work
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- Entire solutions to equivariant elliptic systems with variational structure
- Geometric theory of semilinear parabolic equations
- The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
- A uniform estimate for positive solutions of semilinear elliptic equations
- Some basic facts on the system $\Delta u - W_{u} (u) = 0$
- Symmetric quadruple phase transitions
- A three-layered minimizer in R2 for a variational problem with a symmetric three-well potential
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