ISSN:
1573-2878
Keywords:
Calculus of variations
;
convex functionals
;
rotation groups
;
Fourier transforms
;
Liapunov's theorem
;
radially symmetric solutions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We give some existence results of minima for a class of nonconvex functionals depending on the Laplacian. We minimize these functionals on the set of functionsu inW 2,p (Ω) ∩W 0 1,p (Ω) such that ∂u/∂n=0 on ∂Ω,p〉1, with Ω either an annulus or the whole space ℝ n . Our approach allows us to deal with integrands without any regularity conditions. The results are obtained first by showing that the corresponding convexified problem has at least one radially symmetric solution via a rotation; then, by using a Liapunov's theorem on the range of a vector-valued measure, we construct a function that is a solution to our problem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00940698
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