11 citations · 15 across the 17 of their papers we have counts for
19 papers
Optimal history encoding for elastic-plastic hereditary laws: Sharp input and constitutive approximation
Michael Ortiz, Pablo Pedregal
We formulate rate-independent elastic-ideally-plastic response directly in hereditary form and study its approximation by finite history surrogates. At the material-point level, th…
On a general variational framework for existence and uniqueness in Differential Equations
Pablo Pedregal
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 Di…
A variational approach to Hilbert's 16th problem within the framework of global analysis
Pablo Pedregal
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 ex…
On non-locality in the Calculus of Variations
Pablo Pedregal
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 the…
Inverse quasiconvexification
Pablo Pedregal
In the context of the Calculus of Variations for non-convex, vector variational problems, the natural process of going from a function to its quasiconvexification is quite…
Morrey's conjecture: rank-one convexity implies quasi-convexity for two-dimensional, two-component maps
Pablo Pedregal
We prove that for two-component maps in dimension two, rank-one convexity is equivalent to quasiconvexity. The essential tool for the proof is a fixed-point argument for a suitable…
Hilbert's 16th problem. II. Pfaffian equations and variational methods
Pablo Pedregal
Starting from a Pfaffian equation in dimension and focusing on compact solutions for it, we place in perspective the variational method used in [29] to solve Hilbert's 16th pro…
Hilbert's 16th problem. I. When differential systems meet variational methods
Jaume Llibre, Pablo Pedregal
We provide an upper bound for the number of limit cycles that planar polynomial differential systems of a given degree may have. The bound turns out to be a polynomial of degree fo…
Young-measure solutions for multidimensional systems of conservation laws
Pablo Pedregal
We explore Young measure solutions of systems of conservation laws through an alternative variational method that introduces a suitable, non-negative error functional to measure de…
On a variant of Tykhonov regularization in optimal control under PDEs
Pablo Pedregal
We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and…
About least-squares type approach to address direct and controllability problems
Arnaud Münch, Pablo Pedregal
- We discuss the approximation of distributed null controls for partial differential equations. The main purpose is to determine an approximation of controls that drives the soluti…
Hilbert's 16th problem. When variational principles meet differential systems
Jaume Llibre, Pablo Pedregal
Thanks to the interest of many people, a mistake has been found in our way of counting limit cycles. We are working on a new version.
Constrained optimization through fixed point techniques
Pablo Pedregal
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstraine…
Some evidence in favor of Morrey's conjecture
Pablo Pedregal
We provide further evidence to favor the fact that rank-one convexity does not imply quasiconvexity for two-component maps in dimension two. We provide an explicit family of maps p…
Weak limits in non-linear conductivity
Pablo Pedregal
The problem of characterizing weak limits of sequences of solutions for a non-linear diffusion equation of -laplacian type is addressed. It is formulated in terms of certain mom…
Existence results for optimal control problems with some special non-linear dependence on state and control
Pablo Pedregal, Jorge Tiago
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossi…
A different look at controllability
Pablo Pedregal
We explore further controllability problems through a standard least square approach. By setting up a suitable error functional , and putting for the infimum, we inter…
Optimal feedback control, linear first-order PDE systems, and obstacle problems
Pablo Pedregal
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control probl…
A dynamical-system approach to mathematical programming
Pablo Pedregal
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical syst…