Zobrazeno 1 - 10
of 312
pro vyhledávání: '"Pedregal, Pablo"'
Autor:
Pedregal, Pablo
We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this invariance pr
Externí odkaz:
http://arxiv.org/abs/2411.04552
Autor:
Pedregal, Pablo
We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with some simple
Externí odkaz:
http://arxiv.org/abs/2411.04536
Autor:
Pedregal, Pablo
We focus on optimal control problems governed by elliptic, quasilinear PDEs. Though there are various examples of such problems in the literature, we make an attempt at describing some general principles by dealing with three basic situations. In the
Externí odkaz:
http://arxiv.org/abs/2401.10583
Autor:
Pedregal, Pablo
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some selected exam
Externí odkaz:
http://arxiv.org/abs/2109.06517
Autor:
Pedregal, Pablo
We focus on the second part of Hilbert's 16th problem and provide an upper bound on the number of limit cycles that a polynomial, differential, planar system may have, depending exclusively on the degree $n$ of the system. Such a bound turns out to b
Externí odkaz:
http://arxiv.org/abs/2103.07193
Autor:
Pedregal, Pablo
Non-locality is being intensively studied in various PDE-contexts and in variational problems. The numerical approximation also looks challenging, as well as the application of these models to Continuum Mechanics and Image Analysis, among other areas
Externí odkaz:
http://arxiv.org/abs/2012.10719
Autor:
Pedregal, Pablo
In the context of the Calculus of Variations for non-convex, vector variational problems, the natural process of going from a function $\phi$ to its quasiconvexification $Q\phi$ is quite involved, and, most of the time, an impossible task. We propose
Externí odkaz:
http://arxiv.org/abs/1906.09810
Autor:
Pedregal, Pablo
We prove that, for two-component maps, rank-one convexity is equivalent to quasiconvexity. The essential tool for the proof is a fixed-point argument for a suitable set-valued map going from one component to the other and preserving decomposition dir
Externí odkaz:
http://arxiv.org/abs/1905.06571
Autor:
Pedregal, Pablo
Starting from a Pfaffian equation in dimension $N$ and focusing on compact solutions for it, we place in perspective the variational method used in [29] to solve Hilbert's 16th problem. In addition to exploring how this viewpoint can help in detectin
Externí odkaz:
http://arxiv.org/abs/1904.01300