Uhlenbeck’s Decomposition in Sobolev and Morrey–Sobolev Spaces
Copyright policy )Uhlenbeck’s Decomposition in Sobolev and Morrey–Sobolev Spaces
We present a self-contained proof of Uhlenbeck's decomposition theorem for $��\in L^p(\mathbb{B}^n,so(m)\otimes��^1\mathbb{R}^n)$ for $p\in (1,n)$ with Sobolev type estimates in the case $p \in[n/2,n)$ and Morrey-Sobolev type estimates in the case $p\in (1,n/2)$. We also prove an analogous theorem in the case when $��\in L^p( \mathbb{B}^n, TCO_{+}(m) \otimes ��^1\mathbb{R}^n)$, which corresponds to Uhlenbeck's theorem with conformal gauge group.
- University of Warsaw Poland
Differential forms in global analysis, conformal gauge group, Smoothness and regularity of solutions to PDEs, Nonlinear elliptic equations, A priori estimates in context of PDEs, Sobolev type estimates, Morrey-Sobolev type estimates, Mathematics - Analysis of PDEs, Yang-Mills and other gauge theories in mechanics of particles and systems, 35J45, FOS: Mathematics, Other special methods applied to PDEs, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis of PDEs (math.AP)
Differential forms in global analysis, conformal gauge group, Smoothness and regularity of solutions to PDEs, Nonlinear elliptic equations, A priori estimates in context of PDEs, Sobolev type estimates, Morrey-Sobolev type estimates, Mathematics - Analysis of PDEs, Yang-Mills and other gauge theories in mechanics of particles and systems, 35J45, FOS: Mathematics, Other special methods applied to PDEs, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!