Higher order FEM for the obstacle problem of the p-Laplacian—A variational inequality approach

2018 ◽  
Vol 76 (7) ◽  
pp. 1639-1660 ◽  
Author(s):  
Lothar Banz ◽  
Bishnu P. Lamichhane ◽  
Ernst P. Stephan
Keyword(s):  
Variational Inequality ◽  
Obstacle Problem ◽  
Higher Order

Global weighted Orlicz estimates for irregular obstacle problems with general growth over bounded nonsmooth domains

2018 ◽  
Vol 20 (08) ◽  
pp. 1750083
Author(s):  
Yumi Cho
Keyword(s):  
Variational Inequality ◽  
Sobolev Spaces ◽  
Obstacle Problem ◽  
Obstacle Problems ◽  
Generalized Variational Inequality ◽  
Nonsmooth Domain ◽  
General Growth ◽  
Nonsmooth Domains

We study a generalized variational inequality with an irregular obstacle in the frame of Orlicz–Sobolev spaces. Over a bounded nonsmooth domain having a sufficiently flat boundary in the Reifenberg sense, a global weighted Orlicz estimate is established for the gradient of the solution to the obstacle problem assumed BMO smallness of a coefficient.

scholarly journals A duality-type method for the obstacle problem

2013 ◽  
Vol 21 (3) ◽  
pp. 181-196 ◽  
Author(s):  
Diana Rodica Merlusca
Keyword(s):  
Sobolev Spaces ◽  
Obstacle Problem ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
Higher Order ◽  
Type Method ◽  
Quadratic Optimization Problem ◽  
Approximate Problem ◽  
Duality Property ◽  
New Type

Abstract Based on a duality property, we solve the obstacle problem on Sobolev spaces of higher order. We have considered a new type of approximate problem and with the help of the duality we reduce it to a quadratic optimization problem, which can be solved much easier.

An Obstacle Problem in a Plane Domain with two Solutions

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Giovany M. Figueiredo ◽  
Marcelo Furtado ◽  
Marcelo Montenegro
Keyword(s):  
Variational Inequality ◽  
Obstacle Problem ◽  
Convex Set ◽  
Plane Domain ◽  
Nontrivial Solutions

AbstractWe prove the existence of two nontrivial solutions for the variational inequality∫for every v belonging to some convex set, where Ω ⊂ ℝ

scholarly journals Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Teo Kukuljan
Keyword(s):  
Free Boundary ◽  
Harnack Inequality ◽  
Obstacle Problem ◽  
Linear Equations ◽  
Higher Order ◽  
Second Order ◽  
Boundary Behaviour ◽  
Parabolic Boundary ◽  
Moving Domains

<p style='text-indent:20px;'>We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in <i>C</i><sup>1</sup> and <i>C</i><sup><i>k</i>, <i>α</i></sup> domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary.</p><p style='text-indent:20px;'>As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.</p>

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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