Summer Graduate School

This two week summer school, jointly organized by SLMath with OIST, will offer the following two mini-courses:

1. Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form
   This course will present some recent developments in the theory of divergence-measure fields via measure-theoretic analysis and its applications to the analysis of nonlinear PDEs of conservative form – nonlinear conservation laws.
2. Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs
   This course will present some recent developments precisely characterizing the regularity of the point at ∞ for second order elliptic and parabolic PDEs and broadly extending the role of the Wiener test in classical analysis.

School Structure

Each day will consist of two lectures and two problem sessions; one on each of the above courses.

Suggested Reading List

Prerequisites

1. Basic Measure Theory, Distribution Theory, Sobolev Spaces, Functional Analysis
2. In the graduate textbook: Lawrence C. Evans, Partial Differential Equations, 2nd edition, AMS, 2010:

• Reviewing calculus facts outlined in Appendix C: Calculus
• Reviewing facts outlined in Appendices D and E: Functional Analysis and Measure Theory
• Review Section 2.2. Laplace’s Equation; and Section 2.3. Heat Equation; • Solve exercises 2-17 from Section 2.3 Problems.
• Review Section 2.4, Section 3, and Section 5

Application Procedure

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

For eligibility and how to apply, see the Summer Graduate Schools homepage.

Venue

The summer school will be held at the Okinawa Institute of Science and Technology, Seaside House.