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On the uniqueness of minimal projections in Banach spaces

Szlachtowska E., Mielczarek D.

Opuscula Mathematica

2012

Vol. 32, no. 3

579-590

Let X be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in X and generalized projections acting on X. We prove uniqueness of orthogonal and co-orthogonal projections.

On the solvability of Dirichlet problem for the weighted p-Laplacian

Szlachtowska E.

Opuscula Mathematica

2012

Vol. 32, no. 4

775-781

The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted ρ-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.