Malchiodi, Andrea and Martinazzi, Luca. (2012) Critical points of the MoserTrudinger functional on a disk. Journal of the European Mathematical Society, 16 (5). pp. 893908.
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Official URL: http://edoc.unibas.ch/49907/
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Abstract
On the unit disk B1 subset of R2 we study the MoserTrudinger functional
E(u) = integral(B1) (e(u2)  1)dx, is an element of H0(1) (B1)
and its restrictions E vertical bar MLambda, where MLambda := {u is an element of H0(1) (B1): parallel to u parallel to(2)(H01) = Lambda} for Lambda > 0. We prove that if a sequence u(k) of positive critical points of E vertical bar(M Lambda k) ( for some Lambda(k) > 0) blows up as k > infinity, then Lambda(k) > 4 pi, and u(k) > 0 weakly in H0(1) (B1) and strongly in Cloc(1) ((B) over bar (1) \ {0}).
Using this fact we also prove that when Lambda is large enough, then E vertical bar MLambda has no positive critical point, complementing previous existence results by CarlesonChang, Struwe and LammRobertStruwe.
E(u) = integral(B1) (e(u2)  1)dx, is an element of H0(1) (B1)
and its restrictions E vertical bar MLambda, where MLambda := {u is an element of H0(1) (B1): parallel to u parallel to(2)(H01) = Lambda} for Lambda > 0. We prove that if a sequence u(k) of positive critical points of E vertical bar(M Lambda k) ( for some Lambda(k) > 0) blows up as k > infinity, then Lambda(k) > 4 pi, and u(k) > 0 weakly in H0(1) (B1) and strongly in Cloc(1) ((B) over bar (1) \ {0}).
Using this fact we also prove that when Lambda is large enough, then E vertical bar MLambda has no positive critical point, complementing previous existence results by CarlesonChang, Struwe and LammRobertStruwe.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Mathematik 

UniBasel Contributors:  Martinazzi, Luca 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  European Mathematical Society 
ISSN:  14359855 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Identification Number: 

Last Modified:  22 Jan 2018 10:32 
Deposited On:  22 Jan 2018 10:32 
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