scholarly journals Solutions to equations of {$p$}-Laplacian type in Lorentz spaces

2001 ◽  
Vol 8 (3) ◽  
pp. 469-477
Author(s):  
P. De Nápoli ◽  
M. C. Mariani
Keyword(s):  
Lorentz Spaces ◽  
Solutions To Equations

A genuine analogue of the Wiener Tauberian theorem for some Lorentz spaces on SL(2,ℝ)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tapendu Rana
Keyword(s):  
Tauberian Theorem ◽  
Lorentz Spaces

AbstractIn this paper, we prove a genuine analogue of the Wiener Tauberian theorem for {L^{p,1}(G)} ({1\leq p<2}), with {G=\mathrm{SL}(2,\mathbb{R})}.

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

Complete space-like hypersurfaces in locally symmetric Lorentz spaces

2004 ◽  
Vol 49 (2) ◽  
pp. 231-247 ◽  
Author(s):  
Jin Ok Baek ◽  
Qing-Ming Cheng ◽  
Young Jin Suh
Keyword(s):  
Lorentz Spaces ◽  
Complete Space

scholarly journals Monochromatic solutions to equations with unit fractions

1991 ◽  
Vol 43 (3) ◽  
pp. 387-392 ◽  
Author(s):  
Tom C. Brown ◽  
Voijtech Rödl
Keyword(s):  
Solutions To Equations ◽  
Unit Fractions ◽  
Image Position ◽  
Positive Integers

Our main result is that if G(x1, …, xn) = 0 is a system of homogeneous equations such that for every partition of the positive integers into finitely many classes there are distinct y1,…, yn in one class such that G(y1, …, yn) = 0, then, for every partition of the positive integers into finitely many classes there are distinct Z1, …, Zn in one class such thatIn particular, we show that if the positive integers are split into r classes, then for every n ≥ 2 there are distinct positive integers x1, x1, …, xn in one class such thatWe also show that if [1, n6 − (n2 − n)2] is partitioned into two classes, then some class contains x0, x1, …, xn such that(Here, x0, x2, …, xn are not necessarily distinct.)

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