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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

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

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

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

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

Regularity and Approximability of Electronic Wave Functions Yserentant, Harry | Springer 2010 Nouveau

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

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

Flat level set regularity of p-Laplace phase transitions Valdinoci, Enrico ; Sciunzi, Berardino ; Savin, Vasile Ovidiu | American Mathematical Society 2006 Nouveau

Lectures on Navier-Stokes equations Tsai, Tai-Peng | American Mathematical Society 2018 Nouveau

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

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

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

Réarrangement relatif : un instrument d'estimations dans les problèmes aux limites Rakotoson, Jean-Michel | Springer 2008 Nouveau

Analytic inequalities and their applications in PDEs Qin, Yuming | Birkhäuser 2017 Nouveau

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Boundary value problems of mathematical physics XIV :
collection of papers Ladyzhenskaya, O. A. | American Mathematical Society 1991 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 workshop
Marrakesh # may 10-14, 2010 Barkatou, Y. ; Berhanu, S. ; Meziani, A. ; Meziani, R. ; Mir, N. | American Mathematical Society 2011 Nouveau

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