A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients

2004 ◽  
Vol 56 (6) ◽  
pp. 973-995
Author(s):  
I. I. Skrypnik
Keyword(s):  
Parabolic Equations ◽  
Boundary Point ◽  
Necessary Condition ◽  
Measurable Coefficients

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

On Geodesics in Asymptotic Universal Teichmüller Space

2016 ◽  
Vol 59 (4) ◽  
pp. 1065-1074
Author(s):  
Zhou Zemin ◽  
Chen Jixiu
Keyword(s):  
Boundary Point ◽  
Teichmüller Space ◽  
Equivalence Classes ◽  
Necessary Condition ◽  
Teichmuller Space ◽  
Complex Dilatation ◽  
Universal Teichmüller Space

AbstractLet AT(Δ) be the asymptotic universal Teichmüller space, viewed as the space of all asymptotic Teichmüller equivalence classes [[μ]]. We show that ifμis asymptotically extremal in AT(Δ) andhp([[μ]]) <h([[μ]]) for some boundary pointpofΔ, then there are infinitely many geodesics joining [[0]] and [[μ]] in AT(Δ). As a corollary, a necessary condition for a complex dilatation to be uniquely extremal in AT(Δ) is given.

scholarly journals Parabolic equations with measurable coefficients II

2007 ◽  
Vol 334 (1) ◽  
pp. 534-548 ◽  
Author(s):  
Doyoon Kim
Keyword(s):  
Parabolic Equations ◽  
Measurable Coefficients
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