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
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References
SHOWING 1-10 OF 11 REFERENCES
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…
On a conjecture of De Giorgi concerning nonlinear wave equations
- Mathematics
- 2012
We discuss a conjecture by De Giorgi, which states that global weak solutions to the Cauchy problem associated to certain nonlinear wave equations can be obtained as limits of minimizers of suitable…
Nonlinear wave equations as limits of convex minimization problems: proof of a conjecture by De Giorgi
- Mathematics
- 2012
We prove a conjecture by De Giorgi, which states that global weak solutions of nonlinear wave equations such as w + jwj p 2 w = 0 can be obtained as limits of functions that minimize suitable…
On uniqueness and stability for supercritical nonlinear wave and Schrödinger equations
- Mathematics
- 2006
can be obtained in the a priori much larger class of distribution solutions satisfying the energy inequality. At a conference at the Bernoulli Center of EPFL Lausanne in June 2004, I pointed out that…
Nonlinear Wave Equations
- Mathematics
- 2015
where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F…
Selected Papers
- HistoryNature
- 1949
THIS coluection of papers represents the scientific activities of C. O. Jensen during 1886-1908, and is to be followed by a second volume covering the period 909-33. Thirteen of the papers which were…
A minimization approach to hyperbolic Cauchy problems
- Mathematics
- 2013
Developing an original idea of De Giorgi, we introduce a new and purely variational approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The main novel feature is that…
THE DE GIORGI CONJECTURE ON ELLIPTIC REGULARIZATION
- Mathematics
- 2010
We prove a conjecture by De Giorgi on the elliptic regularization of semilinear wave equations in the finite-time case.
Conjectures concerning some evolution problems
- Duke Math. J
- 1996
Conjectures concerning some evolution problems . A celebration of John F . Nash
- 1996