Article history: Received 26 March 2010 Accepted 9 April 2010 Available online 18 April 2010 Communicated by R. Wu

We consider several differential-topological invariants of compact 4-manifolds which arise directly from Riemannian variational problems. Using recent results of Bauer and Furuta [5, 4], we compute these invariants in many cases that were previously intractable. In particular, we are now able to calculate the Yamabe invariant for certain connected sums of complex surfaces.

We discuss how to solve variational constraint problems involving points, lines and planes. We concentrate on small problems that must be solved simultaneously.

In this paper, by using the variational approach, we study the existence of infinitely many solutions for a class of second-order damped vibration systems under superquadratic and sub-quadratic conditions. Some new results are established and some recent results in the literature are generalized and significantly improved.

In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that...

The energy-integral of the calculus of variations (1.1), (1.2) below has a limit behavior when q = np/(n − p), where p is the harmonic average of the exponents pi, i = 1, . . . , n. In fact, if q is larger than in the stated equality, counterexamples to the local boundedness and regularity of minimizers are known. In this paper we prove the local boundedness of minimizers (and also of quasi-min...

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

We investigate the conditions under which residual-based variational multiscale methods are adjoint, or dual, consistent for model hyperbolic and elliptic partial differential equations. In particular, while many residual-based variational multiscale stabilizations are adjoint consistent for hyperbolic problems and finite-element spaces, only a few are adjoint consistent for elliptic problems.

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The notion of disentangled autoencoders was proposed as an extension to the variational autoencoder by introducing a disentanglement parameter β, controlling the learning pressure put on the possible underlying latent representations. For certain values of β this kind of autoencoders is capable of encoding independent input generative factors in separate elements of the code, leading to a more ...