Boundary modulus of continuity and quasiconformal mappings
Апстракт
Let D be a bounded domain in R-n, n >= 2, and let f be a continuous mapping of (D) over bar into R-n which is quasiconformal in D. Suppose that vertical bar f(x) - f(y)vertical bar LT = omega(vertical bar x-y vertical bar) for all x and y in partial derivative D, where omega is a non-negative non-decreasing function satisfying omega(2t) LT = 2w(t) for t >= 0. We prove, with an additional growth condition on omega, that vertical bar f(x) - f(y)vertical bar LT = C max{omega(vertical bar x - y vertical bar), vertical bar x - y vertical bar(alpha)} for all x, y is an element of D, where alpha = K-1(f)(1/(1-n)).
Кључне речи:
Quasiconformal mapping / modulus of continuityИзвор:
Annales Academiae Scientiarum Fennicae-Mathematica, 2012, 37, 1, 107-118Издавач:
- Suomalainen Tiedeakatemia, Helsinki
Финансирање / пројекти:
- Простори функција и оператори на њима (RS-MESTD-Basic Research (BR or ON)-174017)
- Методе функционалне и хармонијске анализе и ПДЈ са сингуларитетима (RS-MESTD-Basic Research (BR or ON)-174024)
DOI: 10.5186/aasfm.2012.3718
ISSN: 1239-629X
WoS: 000301012300008
Scopus: 2-s2.0-84858711416
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Arsenović, Miloš AU - Todorčević, Vesna AU - Nakki, Raimo PY - 2012 UR - https://rfos.fon.bg.ac.rs/handle/123456789/954 AB - Let D be a bounded domain in R-n, n >= 2, and let f be a continuous mapping of (D) over bar into R-n which is quasiconformal in D. Suppose that vertical bar f(x) - f(y)vertical bar LT = omega(vertical bar x-y vertical bar) for all x and y in partial derivative D, where omega is a non-negative non-decreasing function satisfying omega(2t) LT = 2w(t) for t >= 0. We prove, with an additional growth condition on omega, that vertical bar f(x) - f(y)vertical bar LT = C max{omega(vertical bar x - y vertical bar), vertical bar x - y vertical bar(alpha)} for all x, y is an element of D, where alpha = K-1(f)(1/(1-n)). PB - Suomalainen Tiedeakatemia, Helsinki T2 - Annales Academiae Scientiarum Fennicae-Mathematica T1 - Boundary modulus of continuity and quasiconformal mappings EP - 118 IS - 1 SP - 107 VL - 37 DO - 10.5186/aasfm.2012.3718 UR - conv_1380 ER -
@article{ author = "Arsenović, Miloš and Todorčević, Vesna and Nakki, Raimo", year = "2012", abstract = "Let D be a bounded domain in R-n, n >= 2, and let f be a continuous mapping of (D) over bar into R-n which is quasiconformal in D. Suppose that vertical bar f(x) - f(y)vertical bar LT = omega(vertical bar x-y vertical bar) for all x and y in partial derivative D, where omega is a non-negative non-decreasing function satisfying omega(2t) LT = 2w(t) for t >= 0. We prove, with an additional growth condition on omega, that vertical bar f(x) - f(y)vertical bar LT = C max{omega(vertical bar x - y vertical bar), vertical bar x - y vertical bar(alpha)} for all x, y is an element of D, where alpha = K-1(f)(1/(1-n)).", publisher = "Suomalainen Tiedeakatemia, Helsinki", journal = "Annales Academiae Scientiarum Fennicae-Mathematica", title = "Boundary modulus of continuity and quasiconformal mappings", pages = "118-107", number = "1", volume = "37", doi = "10.5186/aasfm.2012.3718", url = "conv_1380" }
Arsenović, M., Todorčević, V.,& Nakki, R.. (2012). Boundary modulus of continuity and quasiconformal mappings. in Annales Academiae Scientiarum Fennicae-Mathematica Suomalainen Tiedeakatemia, Helsinki., 37(1), 107-118. https://doi.org/10.5186/aasfm.2012.3718 conv_1380
Arsenović M, Todorčević V, Nakki R. Boundary modulus of continuity and quasiconformal mappings. in Annales Academiae Scientiarum Fennicae-Mathematica. 2012;37(1):107-118. doi:10.5186/aasfm.2012.3718 conv_1380 .
Arsenović, Miloš, Todorčević, Vesna, Nakki, Raimo, "Boundary modulus of continuity and quasiconformal mappings" in Annales Academiae Scientiarum Fennicae-Mathematica, 37, no. 1 (2012):107-118, https://doi.org/10.5186/aasfm.2012.3718 ., conv_1380 .