We prove uniqueness of solutions for mean field equations (Caglioti et. Al. Comm. Math. Phys. 174 (1995)) with singular data (Bartolucci et Al. Comm. Math. Phys. 229 (2002)), arising in the analysis of two-dimensional turbulent Euler flows. In this way, we generalize to the singular case some uniqueness results obtained by Chang, Chen and the second author (Chang et. Al. New Stud. Adv. Math. 2 (2003)). In particular, by using a sharp form of an improved Alexandrov-Bol's type isoperimetric inequality, we are able to exploit the role played by the singularities and then obtain uniqueness under weaker boundary regularity assumptions than those assumed in (Chang et. Al. New Stud. Adv. Math. 2 (2003)).
Bartolucci, D., Lin, C. (2009). Uniqueness results for mean field equations with singular data. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 34, 676-702 [10.1080/03605300902910089].
Uniqueness results for mean field equations with singular data
BARTOLUCCI, DANIELE;
2009-01-01
Abstract
We prove uniqueness of solutions for mean field equations (Caglioti et. Al. Comm. Math. Phys. 174 (1995)) with singular data (Bartolucci et Al. Comm. Math. Phys. 229 (2002)), arising in the analysis of two-dimensional turbulent Euler flows. In this way, we generalize to the singular case some uniqueness results obtained by Chang, Chen and the second author (Chang et. Al. New Stud. Adv. Math. 2 (2003)). In particular, by using a sharp form of an improved Alexandrov-Bol's type isoperimetric inequality, we are able to exploit the role played by the singularities and then obtain uniqueness under weaker boundary regularity assumptions than those assumed in (Chang et. Al. New Stud. Adv. Math. 2 (2003)).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
