scholarly journals Maximal regularity via reverse Hölder inequalities for elliptic systems of n-Laplace type involving measures

2008 ◽  
Vol 46 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Tero Kilpeläinen ◽  
Nageswari Shanmugalingam ◽  
Xiao Zhong
Keyword(s):  
Maximal Regularity ◽  
Elliptic Systems ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder ◽  
Laplace Type

scholarly journals Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Na Wei ◽  
Xiangyu Ge ◽  
Yonghong Wu ◽  
Leina Zhao
Keyword(s):  
Weak Solutions ◽  
Vector Fields ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Lp Estimates ◽  
Reverse Hölder Inequalities ◽  
Degenerate Parabolic Systems ◽  
Degenerate Parabolic ◽  
Reverse Hölder ◽  
Nonlinear Degenerate

This paper is devoted to the Lp estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the Lp estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality.

scholarly journals Reverse Hölder Inequalities and Approximation Spaces

2001 ◽  
Vol 109 (1) ◽  
pp. 82-109 ◽  
Author(s):  
Joaquim Martı́n ◽  
Mario Milman
Keyword(s):  
Approximation Spaces ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

scholarly journals Higher integrability for the singular porous medium system

2020 ◽  
Vol 2020 (767) ◽  
pp. 203-230 ◽  
Author(s):  
Verena Bögelein ◽  
Frank Duzaar ◽  
Christoph Scheven
Keyword(s):  
Porous Medium ◽  
Spatial Gradient ◽  
Fast Diffusion ◽  
The Novel ◽  
Higher Integrability ◽  
Reverse Hölder Inequalities ◽  
Diffusion Systems ◽  
Natural Range ◽  
Regularity Results ◽  
Reverse Hölder

AbstractIn this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse Hölder inequality for the gradient. The novel feature in the proof is a suitable intrinsic scaling for space-time cylinders combined with reverse Hölder inequalities and a Vitali covering argument within this geometry. The main result holds for the natural range of parameters suggested by other regularity results. Our result applies to general fast diffusion systems and includes both, non-negative and signed solutions in the case of equations. The methods of proof are purely vectorial in their structure.

scholarly journals Higher integrability and reverse Hölder inequalities in the limit cases

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arturo Popoli
Keyword(s):  
Hölder Inequality ◽  
Muckenhoupt Weights ◽  
Reverse Hölder Inequality ◽  
Higher Integrability ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

Abstract We study the higher integrability of weights satisfying a reverse Hölder inequality ( ⨏ I u β ) 1 β ≤ B ⁢ ( ⨏ I u α ) 1 α {\biggl{(}\fint_{I}u^{\beta}\biggr{)}^{\frac{1}{\beta}}}\leq B{\biggl{(}\fint_{I}u^{\alpha}\biggr{)}^{\frac{1}{\alpha}}} for some B > 1 B>1 and given α < β \alpha<\beta , in the limit cases when α ∈ { - ∞ , 0 } \alpha\in\{-\infty,0\} and/or β ∈ { 0 , + ∞ } \beta\in\{0,+\infty\} . The results apply to the Gehring and Muckenhoupt weights and their corresponding limit classes.

Dyadic weights on $\mathbb {R}^n$ and reverse Hölder inequalities

2016 ◽  
pp. 1-10
Author(s):  
Eleftherios N. Nikolidakis ◽  
Antonios D. Melas
Keyword(s):  
Reverse Hölder Inequalities ◽  
Reverse Hölder

scholarly journals Cotton-Type and Joint Invariants for Linear Elliptic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
A. Aslam ◽  
F. M. Mahomed
Keyword(s):  
Elliptic Equations ◽  
Hyperbolic Equations ◽  
Elliptic Systems ◽  
General System ◽  
Linear Elliptic Equation ◽  
Linear Complex ◽  
Independent Variables ◽  
Joint Invariants ◽  
Laplace Type ◽  
Linear Hyperbolic Equations

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.

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