4 papers
Conjugate harmonic functions in 3D with respect to a unitary gradient
Pablo Pedregal
We propose to relax the classic Cauchy-Riemann equations for a mapping. We support the interest of such a proposal by looking at one specific situation in 3D, and proving the exist…
Invariant Hulls and Geometric Variational Principles
Pablo Pedregal
We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameteri…
Beyond Peano's theorem: a variational look at discontinuous ODE systems
Pablo Pedregal
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 (Pea…
Existence and relaxation for optimal control governed by steady, quasilinear PDEs
Pablo Pedregal
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…