researchseminars.org

Giuseppe Mingione (University of Parma)
2020-05-01 13:00 - 13:50 UTC | https://researchseminars.org/talk/imsseminar/1/
Title: Gradient estimates from uniformly to non-uniformly elliptic problems: part 1 (https://researchseminars.org/talk/imsseminar/1/)
by Giuseppe Mingione (University of Parma) as part of IMS lecture series on regularity theory for quasilinear equations

Abstract
I will give an overview of pointwise gradient estimates for solutions to nonlinear elliptic problems. I will initially recall some results known for uniformly elliptic problems then turning to non-uniformly elliptic ones.

Sun-Sig Byun (Seoul National University)
2020-05-01 14:00 - 14:50 | https://researchseminars.org/talk/imsseminar/2/
Title: Global regularity estimates for nonlinear elliptic equations with nonstandard growth: part 1 (https://researchseminars.org/talk/imsseminar/2/)
by Sun-Sig Byun (Seoul National University) as part of IMS lecture series on regularity theory for quasilinear equations

Abstract
A general class of nonlinear elliptic equations with nonstandard growth in nonsmooth domains is considered for the study of global gradient estimates of solutions.

Sun-Sig Byun (Seoul National University)
2020-05-03 13:00 - 13:50 | https://researchseminars.org/talk/imsseminar/3/
Title: Global regularity estimates for nonlinear elliptic equations with nonstandard growth: Part 2 (https://researchseminars.org/talk/imsseminar/3/)
by Sun-Sig Byun (Seoul National University) as part of IMS lecture series on regularity theory for quasilinear equations

Abstract
A general class of nonlinear elliptic equations with nonstandard growth in nonsmooth domains is considered for the study of global gradient estimates of solutions.

Giuseppe Mingione (University of Parma)
2020-05-02 13:00 - 13:50 | https://researchseminars.org/talk/imsseminar/4/
Title: Gradient estimates from uniformly to non-uniformly elliptic problems: part 2 (https://researchseminars.org/talk/imsseminar/4/)
by Giuseppe Mingione (University of Parma) as part of IMS lecture series on regularity theory for quasilinear equations

Abstract
I will give an overview of pointwise gradient estimates for solutions to nonlinear elliptic problems. I will initially recall some results known for uniformly elliptic problems then turning to non-uniformly elliptic ones.

Nguyen Cong Phuc (Louisiana State University)
2020-05-02 14:00 - 14:50 | https://researchseminars.org/talk/imsseminar/5/
Title: Potential theory and doubly nonlinear PDEs: estimates, existence, and removable sets, part 1 (https://researchseminars.org/talk/imsseminar/5/)
by Nguyen Cong Phuc (Louisiana State University) as part of IMS lecture series on regularity theory for quasilinear equations

Abstract
Recent advances in pointwise potential bounds and integral
weighted estimates are discussed for a class of quasilinear elliptic equations with
measure or distributional data. The connection of those estimates to Sobolev capacities and trace inequalities is presented. Applications include sharp existence criteria and characterizations of removable singular sets for doubly nonlinear equations of the form $-\Delta_p u= u^q +\sigma$, or $-\Delta_p u= |\nabla u|^q +\sigma$. Here $q>0$ could be arbitrarily large, $\Delta_p$ is the $p$-Laplacian ($p>1$), and $\sigma$ is a measure or sometimes a general signed distribution.

Nguyen Cong Phuc (Louisiana State University)
2020-05-03 14:00 - 14:50 | https://researchseminars.org/talk/imsseminar/6/
Title: Potential theory and doubly nonlinear PDEs: estimates, existence, and removable sets, part 2 (https://researchseminars.org/talk/imsseminar/6/)
by Nguyen Cong Phuc (Louisiana State University) as part of IMS lecture series on regularity theory for quasilinear equations

Abstract
Recent advances in pointwise potential bounds and integral
weighted estimates are discussed for a class of quasilinear elliptic equations with
measure or distributional data. The connection of those estimates to Sobolev capacities and trace inequalities is presented. Applications include sharp existence criteria and characterizations of removable singular sets for doubly nonlinear equations of the form $-\Delta_p u= u^q +\sigma$, or $-\Delta_p u= |\nabla u|^q +\sigma$. Here $q>0$ could be arbitrarily large, $\Delta_p$ is the $p$-Laplacian ($p>1$), and $\sigma$ is a measure or sometimes a general signed distribution.
