Non compact variational problems

Academic year 2026/2027
Lecturer Andrea Malchiodi

Examination procedure

seminar relation, oral exam

Examination procedure notes

questions in class, personal appointments

Prerequisites

Functional Analysis, Elliptic Theory, Base notions in

Calculus of Variations. Suggested to Ph.D. students and

V-year Master students.

Syllabus

Introduction and Motivation

Problems with Critical Exponents

Existence of Extremals

Principle of Compactness by Concentration

Minimal and Min-Max Solutions

Time Permitting: Rellich Conjecture






Bibliographical references

Struwe: Variational Methods

Ambrosetti-Malchiodi: Nonlinear Analysis and Semilinear

Elliptic Problems

Aubin: Some nonlinear problems in Riemannian Geometry