### MATH 5041: Topics in Applied Analysis II

**Description:** Advanced topics from the theory of ordinary or partial differential equations. Other possible topics: integral equations, optimization theory, the calculus of variations, advanced approximation theory. With a change of content, this course is repeatable to a maximum of twelve credits.

**Prerequisites:** Instructor consent required.

**Credits:** 3

### MATH 5041 - Section 1: Topics in Applied Analysis II

**Description:** This course intends to cover a number of topics in partial differential equations including: (1) Fundamental solutions to heat equations; Existence and regularity of solutions to parabolic equations of divergence and non-divergence forms; Parabolic Harnack inequalities; Weak and strong maximum principles for parabolic equations. (2) Calculation of variations; Minimizers of the Euler-Lagrange equations of appropriate energy functionals (existence, uniqueness and regularity); harmonic maps.; critical point theory. If time allows, we plan to cover (3) Some nonvariational techniques including fixed point theory, methods of subsolutions/supersolutions, symmetry of solutions and moving plane methods.
Instructor: Guozhen Lu

**Prerequisites:** MATH 5111 and familiarity of Sobolev space theory (say, Chapter 5 of L. C. Evans' PDE book).

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2018 on Storrs Campus

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

15122 | 5041 | 001 | Lecture | TuTh 11:00:00 AM-12:15:00 PM | MONT313 | Lu, Guozhen |