Mappings of generalized finite distortion and continuity
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475605" target="_blank" >RIV/00216208:11320/23:10475605 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rixOG_SXFt" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rixOG_SXFt</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.12835" target="_blank" >10.1112/jlms.12835</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Mappings of generalized finite distortion and continuity
Popis výsledku v původním jazyce
We study continuity properties of Sobolev mappings f is an element of W-loc(1,n )(Omega,R-n),n >= 2, that satisfy the following generalized finite distortion inequality|Df(x)}(n ) <= K(x) J(f)(x)+Sigma(x)for almost every x is an element of R-n. Here K: Omega -> [1,infinity) and Sigma: Omega -> [0,infinity) are measurable functions. Note that when Sigma equivalent to 0, we recover the class of mappings of finite distortion, which are always continuous. The continuity of arbitrary solutions, however, turns out to be an intricate question. We fully solve the continuity problem in the case of bounded distortion K is an element of L-infinity(Omega), where a sharp condition for continuity is that Sigma is in the Zygmund space Sigma log(mu)(e+Sigma)is an element of L-loc(1)(Omega) for some mu > n-1. We also show that one can slightly relax the boundedness assumption on K to an exponential class exp (lambda K) is an element of L-loc(1)(Omega) with lambda > n+1, and still obtain continuous solutions when Sigma log(mu)(e+Sigma)is an element of L-loc(1)(Omega) with mu>lambda. On the other hand, for all p,q is an element of[1,infinity] with p(-1)+q(-1)=1, we construct a discontinuous solution with K is an element of L-loc(p)(Omega) and Sigma/K is an element of L-loc(q)(Omega), including an example with Sigma is an element of L-loc(infinity)(Omega) and K is an element of L-loc(1)(Omega).
Název v anglickém jazyce
Mappings of generalized finite distortion and continuity
Popis výsledku anglicky
We study continuity properties of Sobolev mappings f is an element of W-loc(1,n )(Omega,R-n),n >= 2, that satisfy the following generalized finite distortion inequality|Df(x)}(n ) <= K(x) J(f)(x)+Sigma(x)for almost every x is an element of R-n. Here K: Omega -> [1,infinity) and Sigma: Omega -> [0,infinity) are measurable functions. Note that when Sigma equivalent to 0, we recover the class of mappings of finite distortion, which are always continuous. The continuity of arbitrary solutions, however, turns out to be an intricate question. We fully solve the continuity problem in the case of bounded distortion K is an element of L-infinity(Omega), where a sharp condition for continuity is that Sigma is in the Zygmund space Sigma log(mu)(e+Sigma)is an element of L-loc(1)(Omega) for some mu > n-1. We also show that one can slightly relax the boundedness assumption on K to an exponential class exp (lambda K) is an element of L-loc(1)(Omega) with lambda > n+1, and still obtain continuous solutions when Sigma log(mu)(e+Sigma)is an element of L-loc(1)(Omega) with mu>lambda. On the other hand, for all p,q is an element of[1,infinity] with p(-1)+q(-1)=1, we construct a discontinuous solution with K is an element of L-loc(p)(Omega) and Sigma/K is an element of L-loc(q)(Omega), including an example with Sigma is an element of L-loc(infinity)(Omega) and K is an element of L-loc(1)(Omega).
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Journal of the London Mathematical Society
ISSN
0024-6107
e-ISSN
1469-7750
Svazek periodika
1
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
GB - Spojené království Velké Británie a Severního Irska
Počet stran výsledku
37
Strana od-do
1-37
Kód UT WoS článku
001104130200001
EID výsledku v databázi Scopus
2-s2.0-85176767860