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Lagrange multipliers for functions derivable along directions in a linear subspace


Authors: Le Hai An, Pham Xuan Du, Duong Minh Duc and Phan Van Tuoc
Journal: Proc. Amer. Math. Soc. 133 (2005), 595-604
MSC (2000): Primary 58E05, 49J40, 35J25, 35J60
DOI: https://doi.org/10.1090/S0002-9939-04-07711-1
Published electronically: September 20, 2004
MathSciNet review: 2093084
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Abstract: We prove a Lagrange multipliers theorem for a class of functions that are derivable along directions in a linear subspace of a Banach space where they are defined. Our result is available for topological linear vector spaces and is stronger than the classical one even for two-dimensional spaces, because we only require the differentiablity of functions at critical points. Applying these results we generalize the Lax-Milgram theorem. Some applications in variational inequalities and quasilinear elliptic equations are given.


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Additional Information

Le Hai An
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: anle@math.utah.edu

Pham Xuan Du
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: dxpham@indiana.edu

Duong Minh Duc
Affiliation: Department of Mathematics, Informatics, National University of Hochiminh City, Vietnam
Email: dmduc@hcmc.netnam.vn

Phan Van Tuoc
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: phan@math.umn.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07711-1
Keywords: Lagrange multipliers theorem, Lax-Milgram theorem, variational inequalities, quasilinear elliptic eigenvalue problems
Received by editor(s): February 20, 2003
Published electronically: September 20, 2004
Additional Notes: This work was partially supported by CONACyT (Mexico), grant G36357-E
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2004 American Mathematical Society

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