Superposition operators between Sobolev spaces and a non-existence result of higher-order regular solutions for the p-Laplacian

2015 ◽  
Vol 117 ◽  
pp. 87-98 ◽  
Author(s):  
Florin Isaia
Keyword(s):  
Sobolev Spaces ◽  
Existence Result ◽  
Higher Order ◽  
Regular Solutions ◽  
Superposition Operators

Superposition Operators Between Higher-order Sobolev Spaces and a Multivariate Faà di Bruno Formula: Supercritical Case

2014 ◽  
Vol 14 (1) ◽  
Author(s):  
George Dinca ◽  
Florin Isaia
Keyword(s):  
Sobolev Spaces ◽  
Higher Order ◽  
Supercritical Case ◽  
Superposition Operators ◽  
Faà Di Bruno Formula

AbstractThis paper is a continuation of the work begun in [6] on superposition operators, (N

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

scholarly journals Approximation in higher-order Sobolev spaces and Hodge systems

2019 ◽  
Vol 276 (5) ◽  
pp. 1430-1478 ◽  
Author(s):  
Pierre Bousquet ◽  
Emmanuel Russ ◽  
Yi Wang ◽  
Po-Lam Yung
Keyword(s):  
Sobolev Spaces ◽  
Higher Order

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.

scholarly journals Regular solutions to higher order curvature Einstein–Yang–Mills systems in higher dimensions

2005 ◽  
Vol 22 (24) ◽  
pp. 5201-5222 ◽  
Author(s):  
Peter Breitenlohner ◽  
Dieter Maison ◽  
D H Tchrakian
Keyword(s):  
Higher Dimensions ◽  
Higher Order ◽  
Regular Solutions ◽  
Yang Mills
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