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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

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

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

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

Linear and quasi-linear equations of parabolic type Ladyzenskaja, O. A. ; Solonnikov , V. A. ; Ural'ceva , N. N. | American Mathematical Society 1968 Nouveau

Malliavin calculus for processes with jumps Bichteler, Klaus ; Gravereaux, Jean-Bernard ; Jacod, Jean | Gordon and Breach Sciences Publishers 1987 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

Fine regularity of solutions of elliptic partial differential equations Maly, Jan ; Ziemer, William P. | American Mathematical Society 1997 Nouveau

Nonlinear eigenvalues and analytic-hypoellipticity Yu, Ching-Chau | American Mathematical Society 1998 Nouveau

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

Existence and regularity for nonlinear elastic self-contact problems Von der Mosel, Heiko | Rheinischen Friedrich-Wilhelms-Universität 2002 Nouveau

Aspects of Sobolev-type inequalities Saloff-Coste, Laurent | Cambridge University Press 2002 Nouveau

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

Hölder continuity of weak solutions to subelliptic equations with rough coefficients Sawyer, Eric T. ; Wheeden, Richard L. | American Mathematical Society 2006 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

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