11 citations · 15 across the 17 of their papers we have counts for
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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…