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Research talks;Partial Differential Equations;Probability and Statistics

We are interested in parabolic differential equations $(\partial_t-a\partial_x^2)u=f$ with a very irregular forcing $f$ and only mildly regular coefficients $a$. This is motivated by stochastic differential equations, where $f$ is random, and quasilinear equations, where $a$ is a (nonlinear) function of $u$.
Below a certain threshold for the regularity of $f$ and $a$ (on the Hölder scale), giving even a sense to this equation requires a renormalization. In the framework of the above setting, we present recent ideas from the area of stochastic differential equations (Lyons' rough path, Gubinelli's controlled rough paths, Hairer's regularity structures) that allow to build a solution theory. We make a connection with Safonov's approach to Schauder theory.
This is based on joint work with H. Weber, J. Sauer, and S. Smith. We are interested in parabolic differential equations $(\partial_t-a\partial_x^2)u=f$ with a very irregular forcing $f$ and only mildly regular coefficients $a$. This is motivated by stochastic differential equations, where $f$ is random, and quasilinear equations, where $a$ is a (nonlinear) function of $u$.
Below a certain threshold for the regularity of $f$ and $a$ (on the Hölder scale), giving even a sense to this equation requires a ...

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Documents 35B65 | enregistrements trouvés : 53

Singular SPDE with rough coefficients Otto, Felix | CIRM H Nouveau

Séminaire Bourbaki. Vol. 2008/2009: exposés 997-1011 | Société Mathématique de France 2010 Nouveau

Nonstrictly hyperbolic conservation laws :proceedings of the special session on... held at the 816th meeting of the american mathematical society,in anaheim#Jan. 9-10 Keyfitz, Barbara Lee ; Kranzer, Herbert C. | American Mathematical Society 1987 Nouveau

Geometric analysis of several complex variables and related topics.Proceedings of the workshopMarrakesh # may 10-14, 2010 Barkatou, Y. ; Berhanu, S. ; Meziani, A. ; Meziani, R. ; Mir, N. | American Mathematical Society 2011 Nouveau

Boundary value problems of mathematical physics XIV :collection of papers Ladyzhenskaya, O. A. | American Mathematical Society 1991 Nouveau

Boundary value problems of mathematical physics XIII Ladyzhenskaya, O. A. | American Mathematical Society 1988 Nouveau

Une introduction aux problèmes inverses elliptiques et paraboliques Choulli, Mourad | Springer;Société de Mathématiques Appliquées et Industrielles 2009 Nouveau

Transmission problems for elliptic second-order equations in non-smooth domains Borsuk, Mikhail | Birkhäuser 2010 Nouveau

The Monge-Ampère equation and its applications Figalli, Alessio | European Mathematical Society 2017 Nouveau

The method of Newton's polyhedron in the theory of partial differential equations Gindikin, S. ; Volevich, L. R. | Kluwer Academic Publishers 1992 Nouveau

Smoothness priors analysis of times series Kitagawa, Genshiro ; Gersch, Will | Springer-Verlag 1996 Nouveau

Smoothing and decay estimates for nonlinear diffusion equations :equations of porous medium type Vázquez, Juan Luis | Oxford University Press 2006 Nouveau

Séminaire Bourbaki. Volume 2017/2018:exposés 1136-1150 Bourbaki, Nicolas | Société Mathématique de France 2019 Nouveau

Semilinear Schrödinger equations Cazenave, Thierry | American Mathematical Society 2003 Nouveau

Selected topics in the theory of stability Neustupa, Jiri | Czech Technical University in Prague 1999 Nouveau

Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrations Ruzhansky, M. | Stichting Mathematisch Centrum 2001 Nouveau

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Nonstrictly hyperbolic conservation laws :
proceedings of the special session on... held at the 816th meeting of the american mathematical society,in anaheim#Jan. 9-10 Keyfitz, Barbara Lee ; Kranzer, Herbert C. | American Mathematical Society 1987 Nouveau

Geometric analysis of several complex variables and related topics.
Proceedings of the workshop
Marrakesh # may 10-14, 2010 Barkatou, Y. ; Berhanu, S. ; Meziani, A. ; Meziani, R. ; Mir, N. | American Mathematical Society 2011 Nouveau

Boundary value problems of mathematical physics XIV :
collection of papers Ladyzhenskaya, O. A. | American Mathematical Society 1991 Nouveau

Smoothing and decay estimates for nonlinear diffusion equations :
equations of porous medium type Vázquez, Juan Luis | Oxford University Press 2006 Nouveau

Séminaire Bourbaki. Volume 2017/2018:
exposés 1136-1150 Bourbaki, Nicolas | Société Mathématique de France 2019 Nouveau