# On the extensions of the De Giorgi approach to nonlinear hyperbolic equations

@article{Tentarelli2018OnTE, title={On the extensions of the De Giorgi approach to nonlinear hyperbolic equations}, author={Lorenzo Tentarelli}, journal={arXiv: Analysis of PDEs}, year={2018}, volume={74}, pages={151-160} }

In this talk we present an overview on the extensions of the De Giorgi approach to general second order nonlinear hyperbolic equations. We start with an introduction to the original conjecture by E. De Giorgi (De Giorgi '96) and to its solution by E. Serra and P. Tilli (Serra&Tilli '12). Then, we discuss a first extension of this idea (Serra&Tilli '16) aimed at investigating a wide class of homogeneous equations. Finally, we announce a further extension to nonhomogeneous equations, obtained by…

## 3 Citations

### De Giorgi’s approach to hyperbolic Cauchy problems: The case of nonhomogeneous equations

- Mathematics
- 2017

ABSTRACT In this paper we discuss an extension of some results obtained by Serra and Tilli, in 2012 and 2016, concerning an original conjecture by De Giorgi on a purely minimization approach to the…

### An existence result for dissipative nonhomogeneous hyperbolic equations via a minimization approach

- MathematicsJournal of Differential Equations
- 2019

### Stochastic PDEs via convex minimization

- MathematicsCommunications in Partial Differential Equations
- 2020

Abstract We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle…

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