Search results for " linear growth"
showing 3 items of 3 documents
Nonlinear diffusion in transparent media: the resolvent equation
2017
Abstract We consider the partial differential equation u - f = div ( u m ∇ u | ∇ u | ) u-f=\operatornamewithlimits{div}\biggl{(}u^{m}\frac{\nabla u}{|\nabla u|}% \biggr{)} with f nonnegative and bounded and m ∈ ℝ {m\in\mathbb{R}} . We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ℋ N - 1 {{\mathcal{H}}^{N-1}} -Hausdorff measure. Results and proofs extend to more general nonlinearities.
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
The ends of manifolds with bounded geometry and linear growth
2004
We prove that simply connected open manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.