Lagrange multipliers for functions derivable along directions in a linear subspace

An, Le; Du, Pham; Duc, Duong; Tuoc, Phan Van

doi:10.1090/S0002-9939-04-07711-1

Lagrange multipliers for functions derivable along directions in a linear subspace
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by Le Hai An, Pham Xuan Du, Duong Minh Duc and Phan Van Tuoc PDF

Proc. Amer. Math. Soc. 133 (2005), 595-604 Request permission

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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