A direct approach to the Weiss conjecture for bounded analytic semigroups
We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded -calculus and is based on elementary analysis.
We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded -calculus and is based on elementary analysis.
In this paper we study the finite element approximations to the Sobolev and viscoelasticity type equations and present a direct analysis for global superconvergence for these problems, without using Ritz projection or its modified forms.
In the present paper we give a new proof of the Caffarelli-Kohn-Nirenberg theorem based on a direct approach. Given a pair (u,p) of suitable weak solutions to the Navier-Stokes equations in ℝ³ × ]0,∞[ the velocity field u satisfies the following property of partial regularity: The velocity u is Lipschitz continuous in a neighbourhood of a point (x₀,t₀) ∈ Ω × ]0,∞ [ if for a sufficiently small .
This paper deals with the problem of finding positive solutions to the equation -∆[u] = g(x,u) on a bounded domain 'Omega' with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour. The solutions are found using the Mountain Pass Theorem.