Lower Semicontinuity of Functionals via the Concentration-Compactness Principle

By Eugenio Montefusco. 2001

53 citations recorded by the source corpus.

In this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem. The semicontinuity result allows us to prove several existence results for quasilinear elliptic equations.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/f2baf744ac2b5f8d2092703d531dcdf243037894

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Marco Squassina
2. Wenjing Chen
3. Sunra Mosconi
4. Vicentiu D. Rădulescu
5. Patrick Winkert
6. Binlin Zhang

In Computational Theory and Mathematics

1. Marco Squassina
2. Wenjing Chen
3. Sunra Mosconi
4. Vicentiu D. Rădulescu
5. Patrick Winkert
6. Binlin Zhang

In Control and Systems Engineering

1. Wenjing Chen
2. Marco Squassina
3. Sunra Mosconi

Citations in the corpus

• Nonlocal problems with critical Hardy nonlinearity (2017, background): “In this case we are able to construct sign-changing solution proving the lower-semicontinuity of J via Concentration–Compactess as in [22], at least when μ is below the optimal Hardy constant (coercive case).”