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Existence of cylindrically symmetric ground states to a nonlinear curl-curl equation with non-constant coefficients

Hirsch, Andreas; Reichel, Wolfgang

Abstract:
We consider the nonlinear curl-curl problem ∇ × ∇ × U + V(x)U = f (x, |U|2)U in R3 related to the nonlinear Maxwell equations with Kerr-type nonlinear material laws. We prove the existence of a symmetric ground-state type solution for a bounded, cylindrically symmetric coefficient V and subcritical cylindrically symmetric nonlinearity f . The new existence result extends the class of problems for which ground-state type solutions are known. It is based on compactness properties of symmetric functions [11, 12], new rearrangement type inequalities from [6] and the recent extension of the Nehari-manifold technique from [18].


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000055637
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-556370
KITopen ID: 1000055637
Verlag KIT, Karlsruhe
Umfang 13 S.
Serie CRC 1173 ; 2016/14
Schlagworte curl-curl problem, nonlinear elliptic equations, cylindrical symmetry, variational methods
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