On minima of variational problems with some nonconvex constraints.
Michael Wiegner (1986/1987)
Manuscripta mathematica
Jacob Rubinstein, Michelle Schatzman (1996/1997)
Séminaire de théorie spectrale et géométrie
Nikolaos S. Papageorgiou, George Smyrlis (2003)
Walter Aschbacher, Marco Squassina (2009)
Open Mathematics
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
Peter Laurence, Edward Stredulinsky (1994)
Journal für die reine und angewandte Mathematik
Ramos, Miguel, Soares, Sérgio H.M. (2006)
Portugaliae Mathematica. Nova Série
Paolo Marcellini (1986)
Annales de l'I.H.P. Analyse non linéaire
Zhidkov, P. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Thierry Colin, Michael I. Weinstein (1996)
Annales de l'I.H.P. Physique théorique
Stan Alama, Lia Bronsard, Etienne Sandier (2012)
Journal of the European Mathematical Society
We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting...
J. Chabrowski, Jianfu Yang (2001)
Colloquium Mathematicae
We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.
Jan Chabrowski (2011)
Colloquium Mathematicae
We establish the existence of solutions for the Neumann problem for a system of two equations involving a homogeneous nonlinearity of a critical degree. The existence of a solution is obtained by a constrained minimization with the aid of P.-L. Lions' concentration-compactness principle.
Michael Bildhauer, Martin Fuchs (2007)
Commentationes Mathematicae Universitatis Carolinae
We consider local minimizers of variational integrals like or its degenerate variant with exponents which do not fall completely in the category studied in Bildhauer M., Fuchs M., Calc. Var. 16 (2003), 177–186. We prove interior - respectively -regularity of under the condition that . For decomposable variational integrals of arbitrary order a similar result is established by the way extending the work Bildhauer M., Fuchs M., Ann. Acad. Sci. Fenn. Math. 31 (2006), 349–362.
Bao-Zhu Guo, Zhi-Xiong Zhang (2007)
ESAIM: Control, Optimisation and Calculus of Variations
An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.
Menita Carozza, Antonia Passarelli di Napoli (2000)
Commentationes Mathematicae Universitatis Carolinae
In this paper we prove a regularity result for very weak solutions of equations of the type , where , grow in the gradient like and is not in divergence form. Namely we prove that a very weak solution of our equation belongs to . We also prove global higher integrability for a very weak solution for the Dirichlet problem
Frédéric Hélein (1992)
Banach Center Publications
Christoph Hamburger (2007)
ESAIM: Control, Optimisation and Calculus of Variations
We prove partial regularity with optimal Hölder exponent of vector-valued minimizers u of the quasiconvex variational integral under polynomial growth. We employ the indirect method of the bilinear form.
F. Duzaar, M. Fuchs (1986)
Manuscripta mathematica
Christoph Hamburger (1996)
Annales de l'I.H.P. Analyse non linéaire
Edward Norman Dancer, Shusen Yan (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
The aim of this paper is to study the existence of various types of peak solutions for an elliptic system of FitzHugh-Nagumo type. We prove that the system has a single peak solution, which concentrates near the boundary of the domain. Under some extra assumptions, we also construct multi-peak solutions with all the peaks near the boundary, and a single peak solution with its peak near an interior point of the domain.