Please use this identifier to cite or link to this item:
http://hdl.handle.net/10174/9883
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Title: | POINTWISE CONSTRAINED RADIALLY INCREASING MINIMIZERS IN THE QUASI-SCALAR CALCULUS OF VARIATIONS |
Authors: | Bicho, Luis Ornelas, António |
Editors: | Zuazua, Enrique |
Keywords: | vectorial calculus of variations vectorial distributed-parameter optimal control continuous radially symmetric monotone minimizers |
Issue Date: | 10-Dec-2013 |
Publisher: | ESAIM: COCV |
Abstract: | We prove uniform continuity of radially symmetric vector minimizers uA(x) = UA ( jxj )
to multiple integrals
R
BR
L ( u(x); jDu(x) j ) d x on a ball BR Rd, among the Sobolev
functions u( ) in A + W
1;1
0 (BR; Rm ), using a jointly convex lsc L : Rm R ! [0;1] with
L ( S; ) even and superlinear. Besides such basic hypotheses, L ( ; ) is assumed to satisfy also
a geometrical constraint, which we call quasi scalar ; the simplest example being the biradial
case L ( j u(x) j ; jDu(x) j ). Complete liberty is given for L ( S; ) to take the 1 value, so that
our minimization problem implicitly also represents e.g. distributed parameter optimal control
problems, on constrained domains, under PDEs or inclusions in explicit or implicit form. While
generic radial functions u(x) = U ( jxj ) in this Sobolev space oscillate wildly as jxj ! 0, our minimiz-
ing profilecurve UA( ) is, in contrast, absolutely continuous and tame, in the sense that its \static
level" L (UA(r); 0 ) always increases with r, a original feature of our result. |
URI: | http://hdl.handle.net/10174/9883 |
ISSN: | 1292-8119 |
Type: | article |
Appears in Collections: | CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
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