Phase 1: The lectures

From ISEM 20
Jump to: navigation, search

From 15th October to the middle of February we provide a lecture each week. Our aim is to give a thorough introduction to the field, at a speed suitable for master or Ph.D. students. The weekly lecture will be accompanied by exercises, of which the solutions will be provided by the participants.


Lectures Solutions to Exercises
Lecture 1: Parabolic maximum principle Solutions to Exercises 1
Lecture 2: Semigroups of bounded operators. Part I. Strongly continuous semigroups Solutions to Exercises 2
Lecture 3: Semigroups of bounded operators. Part II. Analytic semigroups Solutions to Exercises 3
Lecture 4: The heat equation and the Gauss-Weierstrass semigroup in C_b(\mathbb R^d). Part 1 Solutions to Exercises 4
Lecture 5: The heat equation and the Gauss-Weierstrass semigroup in C_b(\mathbb R^d). Part 2
Lecture 6: The heat equation and the Gauss-Weierstrass semigroup in C_b(\mathbb R^d). Part 3
Lecture 7: Parabolic equations in \mathbb R^d. Part 1
Lecture 8: Parabolic equations in \mathbb R^d. Part 2 Solutions to Exercises 8
Lecture 9: Parabolic equations in \mathbb R^d. Part 3
Lecture 10: Parabolic equations in \mathbb R^d_+ with homogeneous Dirichlet boundary conditions. Part I (UPDATED VERSION)
Lecture 11: Parabolic equations in \mathbb R^d_+ with homogeneous Dirichlet boundary conditions. Part II
Lecture 12: Parabolic equations in bounded smooth domains \Omega with homogeneous Dirichlet boundary conditions
Lecture 13: The Ornstein-Uhlenbeck operator and its associated semigroup in C_b(\mathbb R^d) (UPDATED VERSION)
Lecture 14: More general elliptic operators with unbounded coefficients Solutions to Exercises 14
Lecture 15: A class on non analytic Markov semigroups on C_b(\mathbb R^d)
Appendix A: Basic notations of functional analysis in Banach spaces
Appendix B: Interior Schauder estimates and optimal Schauder estimates for parabolic problems associated with elliptic operators with unbounded coefficients (UPDATED VERSION)
Appendix C: Proof of Proposition 12.0.4