منابع مشابه
Roughening instability of broken extremals
We derive a new general jump condition on a broken Weierstrass-Erdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does not have a one dimensional analog, reflects the stationarity of the singular surface with respect t...
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In this paper we analyse the optimality of broken Pontryagin extremal for an n -dimensional affine control system with a control parameter, taking values in a k dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the sing...
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We consider optimal control problems with initial–final state equality and inequality constraints and running mixed state-control equality constraints given by smooth functions. The mixed constraints satisfy the regularity assumption of linear independence of gradients with respect to the control. We present simple proofs of second-order necessary conditions for (extended) weak minimum for extr...
متن کاملNonregular Abnormal Extremals
We study existence and rigidity (W1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre-Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extrem...
متن کاملExtremals of Determinants of Laplacians
The modern quantum geometry of strings is concerned to a large extent with the set of all surfaces, with varying metrics on those surfaces, and with determinants of associated Laplacians. Our aim in this paper is to study this determinant as a function of the metric on a given surface and in particular its extreme values when the metric is suitably restricted. This kind of problem has actually ...
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ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2010
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-010-0377-8