Displaying similar documents to “Stability and boundedness of solutions of nonlinear vector differential equations of third order”

Stability of positive part of unit ball in Orlicz spaces

Ryszard Grzaślewicz, Witold Seredyński (2005)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set Q in a topological vector space is stable if the midpoint map Φ : Q × Q → Q , Φ ( x , y ) = ( x + y ) / 2 is open with respect to the inherited topology in Q . The main theorem is established: In the Orlicz space L ϕ ( μ ) the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.

On very weak solutions of a class of nonlinear elliptic systems

Menita Carozza, Antonia Passarelli di Napoli (2000)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we prove a regularity result for very weak solutions of equations of the type - div A ( x , u , D u ) = B ( x , u , D u ) , where A , B grow in the gradient like t p - 1 and B ( x , u , D u ) is not in divergence form. Namely we prove that a very weak solution u ∈ W 1 , r of our equation belongs to W 1 , p . We also prove global higher integrability for a very weak solution for the Dirichlet problem - div A ( x , u , D u ) = B ( x , u , D u ) in Ω , u - u o ∈ W 1 , r ( Ω , ℝ m ) .