### MATH 5010: Topics in Analysis I

**Description:** Advanced topics in analysis. With a change of content, this course is repeatable to a maximum of twelve credits.

**Credits:** 3

### MATH 5010 - Section 1: Geometric Inequalities and Applications to Partial Differential Equations

**Description:** The first half of this course will focus on proofs of geometric inequalities including Sobolev, Poincare and Trudinger-Moser inequalities, etc. We will present some basic tools such as the Marcinkiewicz interpolation theorem, weak and strong type estimates for fractional integrals and use them to prove Poincare and Sobolev inequalities and Trudinger-Moser inequalities. If time allows, we will also prove the best constants for Sobolev and Trudinger-Moser inequalities. The prerequisite for this half is Lebesgue integration theory.

The second half will cover the critical point theory and the mountain pass theorem and use them to study nonlinear partial differential equations with nonlinearity of polynomial growth by Sobolev inequalities and of exponential growth by Trudinger-Moser inequalities.

**Instructor:** Guozhen Lu

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2017 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

19437 | 5010 | 001 | Lecture | TuTh 11:00:00 AM-12:15:00 PM | MONT 245 | Lu, Guozhen |