7 papers
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…
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…
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…