In this note, we discuss symmetry properties of solutions for simple scalar and vector-valued systems of nonlinear elliptic partial dif- ferential equations (PDEs). The systems of interest are of variational nature, they appear, for instance, in some first-order phase transition models in mathematical physics (e.g., phase separation, superconductiv- ity, liquid crystals) and are naturally related to some PDEs in geometry (minimal surfaces and harmonic maps). We review some known results and present few open problems about symmetry of minimizers for all these models.

Symmetry in nonlinear PDEs: Some open problems / Pisante, Adriano. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - STAMPA. - 15:(2014), pp. 299-320. [10.1007/s11784-014-0181-4]

Symmetry in nonlinear PDEs: Some open problems

PISANTE, Adriano
2014

Abstract

In this note, we discuss symmetry properties of solutions for simple scalar and vector-valued systems of nonlinear elliptic partial dif- ferential equations (PDEs). The systems of interest are of variational nature, they appear, for instance, in some first-order phase transition models in mathematical physics (e.g., phase separation, superconductiv- ity, liquid crystals) and are naturally related to some PDEs in geometry (minimal surfaces and harmonic maps). We review some known results and present few open problems about symmetry of minimizers for all these models.
2014
01 Pubblicazione su rivista::01a Articolo in rivista
Symmetry in nonlinear PDEs: Some open problems / Pisante, Adriano. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - STAMPA. - 15:(2014), pp. 299-320. [10.1007/s11784-014-0181-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/655218
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