Search results for "boundary"
showing 10 items of 1626 documents
A Carleson type inequality for fully nonlinear elliptic equations with non-Lipschitz drift term
2017
This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequality proved by the second author in (Julin, ARMA -15), to prove a generalized Carleson estimate. We also prove boundary H\"older continuity and a boundary Harnack type inequality.
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz
2003
Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove that there exists a simple arc gamma joining one of the boundary component of the annulus to the other one, such that gamma is disjoint from its n first iterates under h. As a corollary, we obtain that the rigid rotation of angle alpha can be approximated by homeomorphisms conjugate to h. The first result stated above is an analog of a theorem of J. Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimension…
Nonlinear Robin problems with unilateral constraints and dependence on the gradient
2018
We consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative principle) and approximating the original problem using the Moreau-Yosida approximations of the subdifferential term, we prove the existence of a smooth solution.
Method for Computing Scattering Matrices
2021
Chapter 4 presents statement and justification of a method for approximate computing a waveguide scattering matrix. As an approximation to a row of such a matrix, a minimizer of a quadratic functional is suggested. To construct the functional, one has to solve a boundary value problem in a bounded domain obtained by cutting off the cylindrical ends of the waveguide at distance R. The minimizer tends to the scattering matrix row at exponential rate as R increases to infinity.
Control of essential supremum of solutions of quasilinear degenerate parabolic equations
2001
Sufficient conditions are obtained so that a weak subsolution of a class of quasilinear degenerate parabolic equations, bounded from above on theparabolic boundary of the cylinder Q, turns out to be bounded from above in Q.
Existence results for parametric boundary value problems involving the mean curvature operator
2014
In this note we propose a variational approach to a parametric differential problem where a prescribed mean curvature equation is considered. In particular, without asymptotic assumptions at zero and at infinity on the potential, we obtain an explicit positive interval of parameters for which the problem under examination has at least one nontrivial and nonnegative solution.
New method of grain-boundary extraction by directional optimal filtering: application to estimating creep in metals
2002
It is economically important for manufacturers of high- temperature machines to be able to measure creep so they can predict residual service life more accurately. This paper describes and refines an image analysis method for evaluating creep in laboratory test pieces. It is a preliminary study of how to extract relevant information for creep mea- surement by counting cavities. Sample preparation for quantification by image analysis is an important step determining the further development of the image analysis technique. Grain-boundary extraction, which in- volves directional information, is the major problem to be solved before measurement can be automated. The search for a crest-line extr…
A thermodynamics-based formulation of gradient-dependent plasticity
1998
Abstract A nonlocal thermodynamic theoretical framework is provided as a basis for a consistent formulation of gradient-dependent plasticity in which a scalar internal variable measuring the material isotropic hardening/softening state is the only nonlocal variable. The main concepts of this formulation are: i) the ‘regularization operator’, of differential nature, which governs the relation between the above nonlocal variable and a related local variable (scalar measure of plastic strain) and confers a unified character to the proposed formulation (this transforms into a formulation for nonlocal plasticity if the regularization operator has an integral nature); ii) the ‘nonlocality residua…
A unified residual-based thermodynamic framework for strain gradient theories of plasticity
2011
Abstract A unified thermodynamic framework for gradient plasticity theories in small deformations is provided, which is able to accommodate (almost) all existing strain gradient plasticity theories. The concept of energy residual (the long range power density transferred to the generic particle from the surrounding material and locally spent to sustain some extra plastic power) plays a crucial role. An energy balance principle for the extra plastic power leads to a representation formula of the energy residual in terms of a long range stress, typically of the third order, a macroscopic counterpart of the micro-forces acting on the GNDs (Geometrically Necessary Dislocations). The insulation …
Boundary element solution for free edge stresses in composite laminates
1997
The edge-stress problem in multilayered composite laminates under uniform axial extension is analyzed through an alternative method based on a boundary integral formulation. The basic equations of the formulation are discussed and solved by the multiregion boundary element method. Generalized orthotropic elasticity analytic fundamental solutions are employed to establish the integral equations governing the problem. The formulation is absolutely general with regard to the laminate stacking sequence and the section geometry and it does not require any aprioristic assumption on the elastic response nature. This makes the formulation suitable for an investigation of the singular behavior of th…