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El espacio L1(μ, E).

Alfonsa García López (1987)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis

Maria Alessandra Ragusa (1999)

Commentationes Mathematicae Universitatis Carolinae

In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class H 0 1 , p ( Ω ) for all 1 < p < and, as a consequence, the Hölder regularity of the solution u . is an elliptic second order operator with discontinuous coefficients ( V M O ) and the lower order terms belong to suitable Lebesgue spaces.

Elliptic problems in generalized Orlicz-Musielak spaces

Piotr Gwiazda, Piotr Minakowski, Aneta Wróblewska-Kamińska (2012)

Open Mathematics

We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold

Vladimir A. Mikhailets, Aleksandr A. Murach (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.

Embedding c 0 in bvca ( Σ , X )

Juan Carlos Ferrando, L. M. Sánchez Ruiz (2007)

Czechoslovak Mathematical Journal

If ( Ω , Σ ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that b v c a ( Σ , X ) , the Banach space of all X -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c 0 if and only if X does.

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