MATH517 :       Partial Differential Equations II   (Second term 2017/2018)

Time: Every Wednesday 3pm-6pm, starting from Jan. 3. Location: MATH Annex 1102

Downloads For MATH517

Download 1: Outline

Lecture Note One (Jan. 3): Lecture One

Lecture Note Two (Jan. 10): Lecture Two

Lecture Note Two.5 (Jan. 10): Lecture Two.5

Homework One Homework One

Lecture Note Three (Jan. 24): Lecture Three (Mountain-Pass-Lemma)

Lecture Note Four(Jan. 31): Lecture Four(Limit Case of P.S. Condition, Pohozaev identity, Brezis-Nirenberg Problem, Struwe's Profile Decomposition)

Homework Two Homework Two

Lecture Note Five (Feb.7): Lecture Five (Maximum Principle, Method of Moving Planes)

Lecture Note Six (Feb.28): Lecture Six (Stable Solutions I)

Homework Three Homework Three

Lecture Note Seven (March 7): Lecture Seven (Stable Solutions II)

Homework Four Homework Four (due: March 23)

Lecture Note Eight (March 14): Lecture Eight (Reduction Method)

Homework Five Homework Five (due: April 6)

Update For MATH517

Jan. 3/2018: Reviews: Functional Analysis, Sobolev Spaces, Schauder Theory, W^{2,p} theory, Moser's iteration

Jan. 10/2018: Direct Methods, Direct Methods with constraints, Unbounded domains, Schwartz symmetrization, Strauss Lemma, Brezis-Lieb Lemma.

Jan. 19/2018: Monotone iteration scheme.

Jan. 24/2018: Application of Monotone Iteration Scheme. Start of Mountain-pass-Lemma.

Jan. 31/2018: Mountain-Pass-Lemma. PS sequence. Characterization of mountain-pass value. Section 6: Critical Case. Brezis-Nirenberg. Pohozaev identity.

Feb. 7/2018: Loss of compactness, Brezis-Nirenberg Problem, (dimension n=3 case), Struwe's profile decomposition.

Feb. 14/2018: Completion of Struwe's global decomposition. Maximimum Principles; Method of Mving Planes: Gidas-Ni-Nirenberg. Classification of Yamabe Problem.

Feb. 21/2018: Maximum Principles (Narrow domains, fast-decaying principle). Gidas-Ni-Nirenberg theorem.

Feb. 28/2018: Method of Moving Planes. Classification of Lane-Emden Equations. Supercritical case. Chapter 8: Classification of stable solutions. Neumann boundary condition.

March 7/2018: Classification of stable solutions via Moser's iteration, via Monotonicity formula. Criteria for stable solutions.

March 14/2018: Classification of stable solutions in 2D and 3D.

March 19/2018: Gluing Methods, 9.1 Finite dimensional gluing methods--subcritical case.

March 28/2018: Reduction Methods for subcritical and critical exponent problems. Two methods for reduced problems.

April 04/2018: Infinite dimensional reduction method; (1) geometric setting (2) inner-outer gluing (3) outer problem, (4) inner problem

Downloads For MATH517

The class on Jan. 17 is canceled. Make class one: Jan. 19, 5-6:30pm. MATH Annex 1102.

Make-up class on Jan. 19: 5-6:30pm.

Make-up class on March 19: 4-6:30pm.

Make-up class on April 06: 5:15-6pm.

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