Variational problem involving operator curl associated with p -curl system | Zendy

Junichi Aramaki | Zendy

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Variational problem involving operator curl associated with p -curl system

Author(s) -

Junichi Aramaki

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1606-11

Subject(s) - curl (programming language) , mathematics , vector field , vector operator , bounded function , mathematical analysis , norm (philosophy) , tangent , vector potential , pure mathematics , solenoidal vector field , geometry , computer science , physics , quantum mechanics , political science , magnetic field , law , programming language

We shall study the problem of minimizing a functional involving curl of vector fields in a three-dimensional, bounded multiconnected domain with the prescribed tangent component of a given vector field on the boundary. It will be seen that the minimizers are weak solutions of the p -curl type system. We shall prove the existence and the estimate of minimizers of a more general functional that contains the L norm of the curl of vector fields. We shall also give the continuity with respect to the given data.

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