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A second‐order variational problem with a lack of coercivity
Author(s) -
Moser Roger
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm042
Subject(s) - mathematics , coercivity , order (exchange) , nonlinear system , space (punctuation) , balanced flow , minification , construct (python library) , flow (mathematics) , mathematical analysis , pure mathematics , mathematical optimization , geometry , physics , computer science , condensed matter physics , quantum mechanics , finance , economics , programming language , operating system
For Ω ⊂ ℝ n and 2 n /( n − 2) < p ⩽ (2 n − 4)/( n − 4), we study the functionalE 2 ( u ) = 1 2∫ Ω( Δ u + | u | p − 2 u ) 2 d x .In an appropriate nonlinear space, the minimization problem can be solved using the direct method. We also construct solutions of the gradient flow.