The search session has expired. Please query the service again.
-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness approaches zero of a ferromagnetic thin structure , , whose energy is given bysubject toand to the constraintwhere is any continuous function satisfying -growth assumptions with . Partial results are also obtained in the case , under an additional assumption on .
Γ-convergence techniques and relaxation results of
constrained energy functionals are used to identify the limiting energy as the
thickness ε approaches zero of a ferromagnetic thin
structure , , whose
energy is given by
subject to
and to the constraint
where W is any continuous function satisfying p-growth assumptions
with p> 1.
Partial results are also obtained in the case p=1, under
an additional assumption on W.
We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions...
Integral representation of relaxed energies and of
Γ-limits of functionals
are obtained when sequences of fields v may develop oscillations and are
constrained to satisfy
a system of first order linear partial differential equations. This
framework includes the
treatement of divergence-free fields, Maxwell's equations in
micromagnetics, and curl-free
fields. In the latter case classical relaxation theorems in W1,p, are
recovered.
We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint...
We study integral functionals constrained to divergence-free vector fields in Lp on a thin domain, under standard p-growth and coercivity assumptions, 1 < p < ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in Lp is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint...
In questa nota, si studiano problemi di interpolazione per varietà discrete in spazi di funzioni olomorfe in coni. In particolare si mostra come sia possibile estendere il Principio Fondamentale di Ehrenpreis ad equazioni di convoluzione nella spazio , introdotto in [4] in connessione con problemi di fisica quantistica.
Si estendono qui i risultati della nota precedente al caso di varietà non discrete. Ciò viene utilizzato per ottenere un teorema di rappresentazione per soluzioni di sistemi di equazioni di convoluzione in spazi di funzioni olomorfe in coni.
In this paper we construct a minimizing sequence for the problem (1). In particular, we show that for any subsolution of the Hamilton-Jacobi equation there exists a minimizing sequence weakly convergent to this subsolution. The variational problem (1) arises from the theory of computer vision equations.
On montre l’équivalence entre certaines inégalités “à la Carleman” et certaines propriétés de régularité des solutions à support compact d’équations aux dérivées partielles à coefficients constants : étant un opérateur différentiel sur , on en déduit une caractérisation, en termes d’inégalités , des ouverts de tels que soit -convexe pour tout entier .
is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.
Currently displaying 1 –
20 of
34