Elliptic Systems of Phase Transition Type
About this ebook
Key features and topics of this self-contained, systematic exposition include:
• Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions.
• Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves.
• Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates.
• Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results.
This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.
