scholarly journals Global continuity and higher integrability of a minimizer of an obstacle problem under generalized Orlicz growth conditions

2019 ◽  
Author(s):  
Arttu Karppinen
Keyword(s):  
Obstacle Problem ◽  
Variable Exponent ◽  
Polynomial Growth ◽  
Growth Conditions ◽  
Phase Growth ◽  
Higher Integrability ◽  
Double Phase ◽  
Special Cases

AbstractWe prove continuity up to the boundary of the minimizer of an obstacle problem and higher integrability of its gradient under generalized Orlicz growth. The result recovers similar results obtained in the special cases of polynomial growth, variable exponent growth and produces new results for Orlicz and double phase growth.

scholarly journals Fuglede’s theorem in generalized Orlicz–Sobolev spaces

2021 ◽  
Author(s):  
Jonne Juusti
Keyword(s):  
Sobolev Spaces ◽  
Phase Growth ◽  
Absolutely Continuous ◽  
Double Phase ◽  
Special Cases

AbstractIn this paper, we show that Orlicz–Sobolev spaces $$W^{1,\varphi }(\varOmega )$$ W 1 , φ ( Ω ) can be characterized with the ACL- and ACC-characterizations. ACL stands for absolutely continuous on lines and ACC for absolutely continuous on curves. Our results hold under the assumptions that $$C^1(\varOmega )$$ C 1 ( Ω ) functions are dense in $$W^{1,\varphi }(\varOmega )$$ W 1 , φ ( Ω ) , and $$\varphi (x,\beta ) \ge 1$$ φ ( x , β ) ≥ 1 for some $$\beta > 0$$ β > 0 and almost every $$x \in \varOmega $$ x ∈ Ω . The results are new even in the special cases of Orlicz and double phase growth.

Strain in 3C–SiC Heteroepitaxial Layers Grown on (100) and (111) Oriented Silicon Substrates

2008 ◽  
Vol 600-603 ◽  
pp. 207-210 ◽  
Author(s):  
Marcin Zielinski ◽  
Marc Portail ◽  
Thierry Chassagne ◽  
Yvon Cordier
Keyword(s):  
Gaseous Phase ◽  
Growth Temperature ◽  
Growth Conditions ◽  
Silicon Substrates ◽  
Phase Growth ◽  
Growth Duration ◽  
Strain Control ◽  
Heteroepitaxial Layers ◽  
Oriented Layers ◽  
Sic Films

We discuss the influence of the growth conditions (composition of the gaseous phase, growth duration, growth temperature) and wafer properties (orientation, miscut, thickness) on the residual strain of 3C-SiC films grown on silicon substrates. We show that the strain related effects are observed for both studied orientations however some of them (namely the creep effects) were up to now stated only for (100) oriented layers. We also point out the main difference in strain control between the (111) and (100) orientations.

Effect of anaerobic and stationary phase growth conditions on the heat shock and oxidative stress responses in Escherichia coli K-12

2006 ◽  
Vol 185 (6) ◽  
pp. 429-438 ◽  
Author(s):  
Alondra Díaz-Acosta ◽  
María L. Sandoval ◽  
Luis Delgado-Olivares ◽  
Jorge Membrillo-Hernández
Keyword(s):  
Oxidative Stress ◽  
Escherichia Coli ◽  
Heat Shock ◽  
Stationary Phase ◽  
Stress Responses ◽  
Growth Conditions ◽  
Phase Growth ◽  
K 12 ◽  
Oxidative Stress Responses ◽  
And Oxidative Stress

scholarly journals Approximating graphs with polynomial growth

2000 ◽  
Vol 42 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Norbert Seifter ◽  
Wolfgang Woess
Keyword(s):  
Inverse Limit ◽  
Polynomial Growth ◽  
Infinite Sequence ◽  
Growth Conditions ◽  
Infinite Graph ◽  
Subject Classification ◽  
Transitive Graph ◽  
Locally Finite ◽  
Finite Graphs ◽  
Growth Properties

Let X be an infinite, locally finite, almost transitive graph with polynomial growth. We show that such a graph X is the inverse limit of an infinite sequence of finite graphs satisfying growth conditions which are closely related to growth properties of the infinite graph X.1991 Mathematics Subject Classification. Primary 05C25, Secondary 20F8.

scholarly journals Local higher integrability of the gradient of a quasiminimizer under generalized Orlicz growth conditions

2018 ◽  
Vol 177 ◽  
pp. 543-552 ◽  
Author(s):  
Petteri Harjulehto ◽  
Peter Hästö ◽  
Arttu Karppinen
Keyword(s):  
Growth Conditions ◽  
Higher Integrability

scholarly journals Variational inequalities for energy functionals with nonstandard growth conditions

1998 ◽  
Vol 3 (1-2) ◽  
pp. 41-64 ◽  
Author(s):  
Martin Fuchs ◽  
Li Gongbao
Keyword(s):  
Variational Inequalities ◽  
Obstacle Problem ◽  
Partial Regularity ◽  
Growth Conditions ◽  
Energy Functionals ◽  
Nonstandard Growth ◽  
Bounded Lipschitz Domain ◽  
Growth Properties ◽  
Nonstandard Growth Conditions ◽  
Special Case

We consider the obstacle problem{minimize????????I(u)=?OG(?u)dx??among functions??u:O?Rsuch?that???????u|?O=0??and??u=F??a.e.for a given functionF?C2(O¯),F|?O<0and a bounded Lipschitz domainOinRn. The growth properties of the convex integrandGare described in terms of aN-functionA:[0,8)?[0,8)withlimt?8¯A(t)t-2<8. Ifn=3, we prove, under certain assumptions onG,C1,8-partial regularity for the solution to the above obstacle problem. For the special case whereA(t)=tln(1+t)we obtainC1,a-partial regularity whenn=4. One of the main features of the paper is that we do not require any power growth ofG.

scholarly journals Elliptic problems in variable exponent spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Mihai Mihailescu
Keyword(s):  
Variational Principle ◽  
Nonlinear Elliptic Equation ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Cylindrical Symmetry ◽  
Multiplicity Results ◽  
Variable Exponent Spaces ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

In this paper we study a nonlinear elliptic equation involving p(x)-growth conditions on a bounded domain having cylindrical symmetry. We establish existence and multiplicity results using as main tools the mountain pass theorem of Ambosetti and Rabinowitz and Ekeland's variational principle.

scholarly journals Poincaré inequalities and Neumann problems for the variable exponent setting

2021 ◽  
Vol 4 (5) ◽  
pp. 1-22
Author(s):  
David Cruz-Uribe ◽  
◽  
Michael Penrod ◽  
Scott Rodney ◽  
Keyword(s):  
Variable Exponent ◽  
Growth Conditions ◽  
Linear Elliptic Equation ◽  
Poincaré Inequalities ◽  
Neumann Problems ◽  
Variable Exponent Spaces ◽  
Nonstandard Growth ◽  
Poincare Inequalities ◽  
Nonstandard Growth Conditions ◽  
Weighted Poincaré Inequalities

<abstract><p>In an earlier paper, Cruz-Uribe, Rodney and Rosta proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate $ p $-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate $ {p(\cdot)} $-Laplacian, a non-linear elliptic equation with nonstandard growth conditions.</p></abstract>

scholarly journals An Approximation of Hedberg’s Type in Sobolev Spaces with Variable Exponent and Application

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Aziz Fri
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponent ◽  
Type Equation ◽  
Reaction Diffusion ◽  
Growth Conditions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
New Framework

The aim of this paper is to extend the usual framework of PDE with Au=-div ax,u,∇u to include a large class of cases with Au=∑β≤α-1βDβAβx,u,∇u,…,∇αu, whose coefficient Aβ satisfies conditions (including growth conditions) which guarantee the solvability of the problem Au=f. This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and p-Laplace equation.

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