Conferenciante: María Ángeles García-Ferrero (ICMAT)
Título: "Minimal graphs with micro-oscillations and global approximation theorems in PDEs"
Fecha y hora: Viernes 10 de noviembre de 2017, 12:00
Lugar de encuentro: Seminario 2ª planta, IEMath-GR
In the 1950s, Lax and Malgrange proved that a solution v of a linear elliptic equation with analytic coefficients $Pv=0$ in a compact set can be approximated by a global solution $u$ of $Pu=0$ provided that the complement of the set is connected. This theorem is key to showing the existence of minimal graphs on the unit ball whose transverse intersection with a horizontal hyperplane has arbitrarily large $(n-1)$-measure. The proof hinges on the construction of minimal graphs which are almost flat but have small oscillations of prescribed geometry. In addition, I will present an overview of our recent generalization of the Lax-Malgrange result to the case of parabolic equations and discuss applications to the study of hot spots. This is a joint work with A. Enciso and D. Peralta-Salas.