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Trace operator

In mathematical analysis, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions in a Sobolev space. This is particularly important for the study of partial differential equations with prescribed boundary conditions (boundary value problems), where weak solutions may not be regular…

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Overview

Motivation

Trace theorem

Functions with trace zero

Image of the trace operator

Application

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Map overview Semantic statistics

Trace operator

Nodes42
Edges41
Triples30
Avg. degree1.95
Density0.047619
Components1

How this topic connects Entity context

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Trace operator

Top relations

related to Construction · 8
Trace operator → By, Evans, Gagliardo, Lipschitz, Omega, On, The, This
related to Higher derivatives · 6
Trace operator → Let, Many, Omega, Similar, Since, Then
related to Trace theorem · 6
Trace operator → Let, Lipschitz, Omega, Sobolev, The, Then
related to For p > 1 · 4
Trace operator → As, Hölder, Omega, The
related to Right-inverse: trace extension operator · 4
Trace operator → Omega, Sobolev-Slobodeckij, Specifically, The
related to For p = 1 · 2
Trace operator → For, Omega

Important terminology Word statistics

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Important terminology

textstyle omega trace operator partial functions domain bounded infty boundary subset space extension mathbb exists spaces linear bar weak image

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Trace operatorrelated to ConstructionThis0.60section
Trace operatorrelated to ConstructionEvans0.60section
Trace operatorrelated to ConstructionOmega0.60section
Trace operatorrelated to ConstructionLipschitz0.60section
Trace operatorrelated to ConstructionGagliardo0.60section
Trace operatorrelated to ConstructionOn0.60section
Trace operatorrelated to ConstructionBy0.60section
Trace operatorrelated to ConstructionThe0.60section
Trace operatorrelated to For p = 1For0.60section
Trace operatorrelated to For p = 1Omega0.60section
Trace operatorrelated to For p > 1The0.60section
Trace operatorrelated to For p > 1Omega0.60section

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    Min side: 3
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