caa a22 4500 445843497 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00526-010-0349-8 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0349-8 Local minimizers and planar interfaces in a phase-transition model with interfacial energy [Elektronische Daten] [J. Ball, E. Crooks] Interfacial energy is often incorporated into variational solid-solid phase transition models via a perturbation of the elastic energy functional involving second gradients of the deformation. We study consequences of such higher-gradient terms for local minimizers and for interfaces. First it is shown that at slightly sub-critical temperatures, a phase which globally minimizes the elastic energy density at super-critical temperatures is an L 1-local minimizer of the functional including interfacial energy, whereas it is typically only a W 1,∞-local minimizer of the purely elastic functional. The second part deals with the existence and uniqueness of smooth interfaces between different wells of the multi-well elastic energy density. Attention is focussed on so-called planar interfaces, for which the deformation depends on a single direction x · N and the deformation gradient then satisfies a rank-one ansatz of the form $${Dy(x) = A + u(x \cdot N) \otimes N}$$ , where A and $${B=A+a \otimes N}$$ are the gradients connected by the interface. Springer-Verlag, 2010 Ball J. Mathematical Institute, University of Oxford, 24-29 St. Giles', OX1 3LB, Oxford, UK aut Crooks E. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK aut Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 501-538 0944-2669 40:3-4<501 2011 40 526 https://doi.org/10.1007/s00526-010-0349-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0349-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ball J. Mathematical Institute, University of Oxford, 24-29 St. Giles', OX1 3LB, Oxford, UK aut NATIONALLICENCE 700 1- Crooks E. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, UK aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 501-538 0944-2669 40:3-4<501 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer