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Chinese Annals of Mathematics, Series B : Volume 38

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Chinese Annals of Mathematics, Series B : Volume 34

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Chinese Annals of Mathematics, Series B : Volume 34, Issue 5, September 2013

Operator equations and duality mappings in Sobolev spaces with variable exponents

A variational finite element model for large-eddy simulations of turbulent flows

A note on the essential norm of composition operators from H $^{ p }$(B $_{ N }$) to H $^{ q }$(B $_{ N }$)

Existence of classical solutions to a stationary simplified quantum energy-transport model in 1-dimensional space

On the Buchstaber invariant of simple convex 3-polytopes

On the Diophantine equation x $^{2}$ − kxy + y $^{2}$ + lx = 0

Uniqueness theorems for meromorphic mappings in several complex variables into P $^{ N }$(ℂ) with two families of moving targets

Stochastic H $_{2}$/H $_{∞}$ control with random coefficients

Curvature estimates of hypersurfaces in the Minkowski space

On the ratio between 2-domination and total outer-independent domination numbers of trees

Recognizing finite groups through order and degree patterns

Some subsystems of a lie triple system closely related to its Frattini subsystem

Chinese Annals of Mathematics, Series B : Volume 34, Issue 4, July 2013

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Chinese Annals of Mathematics, Series B : Volume 34, Issue 2, March 2013

Chinese Annals of Mathematics, Series B : Volume 34, Issue 1, January 2013

Chinese Annals of Mathematics, Series B : Volume 33

Chinese Annals of Mathematics, Series B : Volume 32

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Chinese Annals of Mathematics, Series B : Volume 30

Chinese Annals of Mathematics, Series B : Volume 29

Chinese Annals of Mathematics, Series B : Volume 28

Chinese Annals of Mathematics, Series B : Volume 27

Operator equations and duality mappings in Sobolev spaces with variable exponents

Content Provider	Springer Nature Link
Author	Ciarlet, Philippe G. Dinca, George Matei, Pavel
Copyright Year	2013
Abstract	After studying in a previous work the smoothness of the space $U_{\Gamma _0 } = \{ u \in W^{1,p( \cdot )} (\Omega );u = 0on\Gamma _0 \subset \Gamma = \partial \Omega \} ,$ where dΓ − measΓ$_{0}$ > 0, with p(·) ∈ $\mathcal{C}(\bar \Omega )$ and p(x) > 1 for all x ∈ $\bar \Omega $ , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form J $_{φ}$ u = N, where J $_{φ}$ is a duality mapping on $U_{\Gamma _0 } $ corresponding to the gauge function φ, and N $_{ f }$ is the Nemytskij operator generated by a Carathéodory function f satisfying an appropriate growth condition ensuring that N $_{ f }$ may be viewed as acting from $U_{\Gamma _0 } $ into its dual.
Starting Page	639
Ending Page	666
Page Count	28
File Format	PDF
ISSN	02529599
Journal	Chinese Annals of Mathematics, Series B
Volume Number	34
Issue Number	5
e-ISSN	18606261
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-07-19
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Monotone operators Smoothness Strict convexity Uniform convexity Duality mappings Sobolev spaces with a variable exponent Nemytskij operators Nonlinear elliptic equations Boundary value problems for second-order elliptic equations Partial differential operators Mathematics Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions

Existence and multiplicity of solutions to operator equations involving duality mappings on Sobolev spaces with variable exponents

Second-order boundary-value problems with variable exponents

Lipschitz properties in variable exponent problems via relative rearrangement

Problem with Critical Sobolev Exponent and with Weight

Optimal Sobolev Regularity for Linear Second-Order Divergence Elliptic Operators Occurring in Real-World Problems

Entropy solution for nonlinear elliptic problem involving variable exponent and Fourier type boundary condition

The Neumann Problem for Semilinear Elliptic Equations with Critical Sobolev Exponent

Variable Exponent Sobolev Spaces for Semilinear Elliptic Systems

Operator equations and duality mappings in Sobolev spaces with variable exponents

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