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.
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).
Sections: Spring 2018 on Storrs Campus
|15122||5041||001||Lecture||TuTh 11:00:00 AM-12:15:00 PM||Lu, Guozhen|