SCAPDE

Semi-Classical Analysis and Partial Differential Equations

 Coordinatore UNIVERSITE DE NICE SOPHIA ANTIPOLIS 

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 Nazionalità Coordinatore France [FR]
 Totale costo 1˙705˙750 €
 EC contributo 1˙705˙750 €
 Programma FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call ERC-2012-ADG_20120216
 Funding Scheme ERC-AG
 Anno di inizio 2013
 Periodo (anno-mese-giorno) 2013-05-01   -   2018-04-30

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITE DE NICE SOPHIA ANTIPOLIS

 Organization address address: AVENUE VALROSE 28 GRAND CHATEAU
city: NICE
postcode: 6100

contact info
Titolo: Mr.
Nome: Gilles
Cognome: Lebeau
Email: send email
Telefono: +33 4 92 07 62 43
Fax: +33 4 93 51 79 74

FR (NICE) hostInstitution 1˙705˙750.00

Mappa


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domains    differential    pde    tools    linear    semi    theory    equations    probability    dispersive    estimates    boundary   

 Obiettivo del progetto (Objective)

'Semi-classical analysis started to be developed about 50 years ago by the works of Sato and Hormander on micro-local analysis. Nowadays, it has reached great achievement with many applications to different topics in analysis including spectral theory, scattering theory, control theory, and some aspects in non linear equations, by the use of dispersive estimates and paraproduct techniques .

The objective of our proposal is to develop new tools and applications in two directions : boundary value problems and connections between probability and semi-classical analysis. We expect to solve basic remaining open problems in the analysis of boundary problems, and to make contributions to develop new links between probability and analysis of partial differential equations.

We will focus on four topics : - 1) Dispersive and Strichartz estimates for wave or Schrödinger equations in domains. Applications to the Cauchy problem for non linear waves in domains. - 2) Theoretical analysis of the optimal control operator in control theory. - 3) Analysis of Markov Chain Monte Carlo algorithm of Metropolis type via PDE's tools. - 4) Applications of probabilistic tools to the analysis of PDE.

Topics 1) and 2) are strongly connected to progress in the analysis of boundary value problems. Topic 3) involves a generalization of the classical pseudo-differential calculus. The purpose of topic 4) is to develop a new field of research for deterministic PDE's (and therefore is not in the area of stochastic PDE's).

All topics involve geometric analysis in the phase space.'

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