Lecture notes

• 5. Homogenization and Selection Problems for Hamilton–Jacobi Equations — 2026 UC Irvine Summer School on Theory and Applications of Elliptic PDE first draft.
• 4. A topic course on viscosity solutions (Math 821 at UW) first draft.
• 3. (with Y. Yu) A course on weak KAM theory — first draft.
• 2. Hamilton–Jacobi equations: Theory and Applications, AMS Graduate Studies in Mathematics — third draft.
  Note that the published version will be a bit different from my third draft. Earlier versions with a slightly different name are as follows:
  Hamilton–Jacobi equations: viscosity solutions and applications
  First draft (April 2019).
  Second draft (updated regularly over Summer 2019).
• 1. (with H. Mitake) Dynamical properties of Hamilton–Jacobi equations via the nonlinear adjoint method: Large time behavior and Discounted approximation — pdf (updated version, 12/2016), Springer Lecture Notes in Mathematics.

Others

• 1. Lecture notes for an undergraduate PDE course (Math 619 at UW): brief notes.
  Class lecture notes taken by Chenyang Zhang: Chenyang Zhang's notes.
• 2. Lecture notes for Math 821: a topic course on viscosity solutions (handwritten notes by Hieu Nguyen).
  First-order Hamilton–Jacobi equations: Part 1, Part 2.
  Fully nonlinear elliptic/parabolic equations: Part 3, Part 4.
  Level set mean curvature flow PDE: Part 5.
• 3. Lecture notes for Math 807, a course on weak KAM theory (typed up by Son Tu): pdf.
• 4. Notes and Remarks, by Son Nguyen Thai Tu and Son Phung Truong Van, on an introductory course on periodic homogenization of Hamilton–Jacobi equations that I gave in Summer 2015.
• 5. A note on weak convergence method, by Doanh Pham.
• 6. Ergodic problems for Hamilton–Jacobi equations, by Minh Hoang Le and Minh-Quan Hoang Vu.
• 7. Fixed points method and applications to ODEs and PDEs, by Daotong Ge.
• 8. Notes for Analysis I (Math 521), by Emmett Galles.