Let Omega subset of R-2 be a bounded domain with the same area as the unit disk B-1 and letE-epsilon(u, Omega) = 1/2 integral(Omega) vertical bar del u vertical bar(2) dx + 1/4 epsilon(2) integral(Omega) (vertical bar u vertical bar(2) - 1)(2) dxbe the Ginzburg-Landau functional. Denote by (u) over tilde (epsilon) the radial solution to the Euler equation associated to the problem min {E-epsilon (u, B-1) : u vertical bar(partial derivative B1) = x} and byK = {v = (v(1), v(2)) is an element of H-1 (Omega; R-2) : integral(Omega) v(1) dx = integral(Omega) v(2) dx = 0,integral(Omega) vertical bar v vertical bar(2) dx >= integral(B1) vertical bar(u) over tilde vertical bar(2) dx}.In this note we prove thatmin(v is an element of K) E-epsilon (v, Omega) <= E-epsilon ((u) over tilde, B-1).

Brandolini, B., & Chiacchio, F. (2014). A REMARK ON THE RADIAL MINIMIZER OF THE GINZBURG-LANDAU FUNCTIONAL. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 224, 1-4.

A REMARK ON THE RADIAL MINIMIZER OF THE GINZBURG-LANDAU FUNCTIONAL

Brandolini, B
;
2014

Abstract

Let Omega subset of R-2 be a bounded domain with the same area as the unit disk B-1 and letE-epsilon(u, Omega) = 1/2 integral(Omega) vertical bar del u vertical bar(2) dx + 1/4 epsilon(2) integral(Omega) (vertical bar u vertical bar(2) - 1)(2) dxbe the Ginzburg-Landau functional. Denote by (u) over tilde (epsilon) the radial solution to the Euler equation associated to the problem min {E-epsilon (u, B-1) : u vertical bar(partial derivative B1) = x} and byK = {v = (v(1), v(2)) is an element of H-1 (Omega; R-2) : integral(Omega) v(1) dx = integral(Omega) v(2) dx = 0,integral(Omega) vertical bar v vertical bar(2) dx >= integral(B1) vertical bar(u) over tilde vertical bar(2) dx}.In this note we prove thatmin(v is an element of K) E-epsilon (v, Omega) <= E-epsilon ((u) over tilde, B-1).
Settore MAT/05 - Analisi Matematica
http://ejde.math.txstate.edu
Brandolini, B., & Chiacchio, F. (2014). A REMARK ON THE RADIAL MINIMIZER OF THE GINZBURG-LANDAU FUNCTIONAL. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 224, 1-4.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/494011
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