Calculus of Variations and Geometric Measure Theory

L. Tentarelli - P. Tilli

De Giorgi's approach to hyperbolic Cauchy problems: the case of nonhomogeneous equations

created by tentarelli on 07 Jul 2022


Published Paper

Inserted: 7 jul 2022
Last Updated: 7 jul 2022

Journal: Comm. Partial Differential Equations
Volume: 43
Number: 4
Pages: 677-698
Year: 2018
Doi: 10.1080/03605302.2018.1459686

ArXiv: 1709.09111 PDF


In this paper we discuss an extension of some results obtained by E. Serra and P. Tilli, in Serra&Tilli '12, Serra&Tilli '16, concerning an original conjecture by E. De Giorgi (De Giorgi '96, De Giorgi '06) on a purely minimization approach to the Cauchy problem for the defocusing nonlinear wave equation. Precisely, we show how to extend the techniques developed by Serra and Tilli for homogeneous hyperbolic nonlinear PDEs to the nonhomogeneous case, thus proving that the idea of De Giorgi yields in fact an effective approach to investigate general hyperbolic equations.