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Erschienen in:
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2019 | OriginalPaper | Buchkapitel

7. Special Cases

verfasst von : Petteri Harjulehto, Peter Hästö

Erschienen in: Orlicz Spaces and Generalized Orlicz Spaces

Verlag: Springer International Publishing

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Abstract

In this chapter, we consider our conditions and results in some special cases, namely variable exponent spaces and their variants, for double phase and degenerate double phase growth, as well as for Orlicz growth without x-dependence.

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Vorheriges Kapitel Sobolev Spaces
Literatur
1.
T. Adamowicz, O. Toivanen, Hölder continuity of quasiminimizers with nonstandard growth. Nonlinear Anal. 125, 433–456 (2015)MathSciNetCrossRef
4.
Y. Ahmida, I. Chlebicka, P. Gwiazda, A. Youssfi, Gossez’s approximation theorems in Musielak-Orlicz-Sobolev spaces. J. Funct. Anal. 275(9), 2538–2571 (2018)MathSciNetCrossRef
7.
P. Baroni, M. Colombo, G. Mingione, Harnack inequalities for double phase functionals. Nonlinear Anal. 121, 206–222 (2015)MathSciNetCrossRef
8.
P. Baroni, M. Colombo, G. Mingione, Nonautonomous functionals, borderline cases and related function classes. Algebra i Analiz 27(3), 6–50 (2015)MathSciNetMATH
9.
P. Baroni, M. Colombo, G. Mingione, Regularity for general functionals with double phase. Calc. Var. Partial Differ. Equ. 57(2), Art. 62 (2018)
10.
A.C. Barroso, E. Zappale, Relaxation for optimal design problems with non-standard growth. Appl. Math. Optim. (2018)
13.
S.-S. Byun, Y. Cho, J. Oh, Gradient estimates for double phase problems with irregular obstacles. Nonlinear Anal. 177(part A), 169–185 (2018)MathSciNetCrossRef
16.
S.-S. Byun, Y. Youn, Riesz potential estimates for a class of double phase problems. J. Differ. Equ. 264(2), 1263–1316 (2018)MathSciNetCrossRef
17.
C. Capone, D. Cruz-Uribe, A. Fiorenza, A modular variable Orlicz inequality for the local maximal operator. Georgian Math. J. 25(2), 201–206 (2018)MathSciNetCrossRef
18.
R.E. Castillo, H. Rafeiro, An Introductory Course in Lebesgue Spaces. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC (Springer, Cham, 2016)
19.
M. Cencelj, V.D. Rădulescu, D.D. Repovš, Double phase problems with variable growth. Nonlinear Anal. 177(part A), 270–287 (2018)MathSciNetCrossRef
22.
I. Chlebicka, P. Gwiazda, A. Zatorska-Goldstein, Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak-Orlicz spaces in the class of renormalized solutions. J. Differ. Equ. 265(11), 5716–5766 (2018)MathSciNetCrossRef
24.
F. Colasuonno, M. Squassina, Eigenvalues for double phase variational integrals. Ann. Mat. Pura Appl. (4) 195(6), 1917–1959 (2016)MathSciNetCrossRef
25.
M. Colombo, G. Mingione, Bounded minimisers of double phase variational integrals. Arch. Ration. Mech. Anal. 218(1), 219–273 (2015)MathSciNetCrossRef
26.
M. Colombo, G. Mingione, Regularity for double phase variational problems. Arch. Ration. Mech. Anal. 215(2), 443–496 (2015)MathSciNetCrossRef
27.
D. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis (Birkhäuser, Basel, 2013)CrossRef
34.
L. Diening, P. Harjulehto, P. Hästö, M. Růžička, Lebesgue and Sobolev spaces with Variable Exponents, volume 2017 of Lecture Notes in Mathematics (Springer, Heidelberg, 2011)MATH
38.
D.E. Edmunds, J. Lang, O. Méndez, Differential Operators on Spaces of Variable Integrability (World Scientific Publishing, Hackensack, NJ, 2014)CrossRef
43.
F. Giannetti, A. Passarelli di Napoli, Regularity results for a new class of functionals with non-standard growth conditions. J. Differ. Equ. 254(3), 1280–1305 (2013)MathSciNetCrossRef
44.
F. Giannetti, A. Passarelli di Napoli, M.A. Ragusa, A. Tachikawa, Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth. Calc. Var. Partial Differ. Equ. 56(6), Art. 153, 29 (2017)
45.
F. Giannetti, A. Passarelli di Napoli, A. Tachikawa, Partial regularity results for non-autonomous functionals with Φ-growth conditions. Ann. Mat. Pura Appl. (4) 196(6), 2147–2165 (2017)
47.
R. Giova, Regularity results for non-autonomous functionals with \(L\log L\)-growth and Orlicz Sobolev coefficients. NoDEA Nonlinear Differ. Equ. Appl. 23(6):Art. 64, 18 (2016)
48.
P. Gwiazda, I. Skrzypczak, A. Zatorska-Goldstein, Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space. J. Differ. Equ. 264(1), 341–377 (2018)MathSciNetCrossRef
54.
P. Harjulehto, P. Hästö, Boundary regularity under generalized growth conditions. Z. Anal. Anwend. 38(1), 73–96 (2019)MathSciNetCrossRef
57.
P. Harjulehto, P. Hästö, M. Lee, Hölder continuity of quasiminimizers and ω-minimizers of functionals with generalized Orlicz growth. Preprint (2018)
58.
P. Harjulehto, P. Hästö, O. Toivanen, Hölder regularity of quasiminimizers under generalized growth conditions. Calc. Var. Partial Differ. Equ. 56(2), Art. 22 (2017)
61.
P. Hästö, J. Ok, Maximal regularity for local minimizers of non-autonomous functionals. Preprint (2019)
66.
R. Hurri-Syrjänen, A generalization of an inequality of Bhattacharya and Leonetti. Can. Math. Bull. 39(4), 438–447 (1996)MathSciNetCrossRef
67.
Y. Karagiorgos, N. Yannakakis, A Neumann problem involving the p(x)-Laplacian with p = ∞ in a subdomain. Adv. Calc. Var. 9(1), 65–76 (2016)MathSciNetMATH
68.
Y. Karagiorgos, N. Yannakakis, A Neumann problem for the p(x)-Laplacian with p = 1 in a subdomain. J. Math. Anal. Appl. 454(1), 412–428 (2017)MathSciNetCrossRef
70.
A. Karapetyants, S. Samko, On boundedness of Bergman projection operators in Banach spaces of holomorphic functions in half-plane and harmonic functions in half-space. J. Math. Sci. (N.Y.) 226(4, Problems in mathematical analysis. No. 89 (Russian)), 344–354 (2017)MathSciNetCrossRef
72.
V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko, Integral Operators in Non-standard Function Spaces. Vol. 1, volume 248 of Operator Theory: Advances and Applications (Birkhäuser/Springer, Cham, 2016). Variable exponent Lebesgue and amalgam spacesMATH
73.
V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko, Integral Operators in Non-standard Function Spaces. Vol. 2, volume 249 of Operator Theory: Advances and Applications (Birkhäuser/Springer, Cham, 2016). Variable exponent Hölder, Morrey-Campanato and grand spacesMATH
79.
F.-Y. Maeda, Y. Mizuta, T. Ohno, T. Shimomura, Approximate identities and Young type inequalities in Musielak-Orlicz spaces. Czech. Math. J. 63(138)(4), 933–948 (2013)MathSciNetCrossRef
87.
F.-Y. Maeda, Y. Sawano, T. Shimomura, Some norm inequalities in Musielak-Orlicz spaces. Ann. Acad. Sci. Fenn. Math. 41(2), 721–744 (2016)MathSciNetCrossRef
92.
Y. Mizuta, E. Nakai, T. Ohno, T. Shimomura, Hardy’s inequality in Orlicz-Sobolev spaces of variable exponent. Hokkaido Math. J. 40(2), 187–203 (2011)MathSciNetCrossRef
93.
Y. Mizuta, T. Ohno, T. Shimomura, Sobolev’s inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot )}(\log L)^{q(\cdot )}\). J. Math. Anal. Appl. 345(1), 70–85 (2008)
94.
Y. Mizuta, T. Ohno, T. Shimomura, Sobolev inequalities for Musielak-Orlicz spaces. Manuscripta Math. 155(1–2), 209–227 (2018)MathSciNetCrossRef
95.
Y. Mizuta, T. Shimomura, A trace inequality of Riesz potentials in variable exponent Orlicz spaces. Math. Nachr. 285(11–12), 1466–1485 (2012)MathSciNetMATH
100.
A. Nekvinda, Hardy-Littlewood maximal operator on \(L^{p(x)}({\mathbb {R}^n})\). Math. Inequal. Appl. 7, 255–266 (2004)
102.
T. Ohno, T. Shimomura, Trudinger’s inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces. Nonlinear Anal. 106, 1–17 (2014)MathSciNetCrossRef
107.
T. Ohno, T. Shimomura, Boundary limits of monotone Sobolev functions in Musielak-Orlicz spaces on uniform domains in a metric space. Kyoto J. Math. 57(1), 147–164 (2017)MathSciNetCrossRef
108.
J. Ok, Calderón-Zygmund estimates for a class of obstacle problems with nonstandard growth. NoDEA Nonlinear Differ. Equ. Appl. 23(4), Art. 50, 21 (2016)
110.
J. Ok, Regularity results for a class of obstacle problems with nonstandard growth. J. Math. Anal. Appl. 444(2), 957–979 (2016)MathSciNetCrossRef
111.
J. Ok, Regularity of ω-minimizers for a class of functionals with non-standard growth. Calc. Var. Partial Differ. Equ. 56(2), Art. 48, 31 (2017)
112.
J. Ok, Partial Hölder regularity for elliptic systems with non-standard growth. J. Funct. Anal. 274(3), 723–768 (2018)MathSciNetCrossRef
114.
K. Perera, M. Squassina, Existence results for double-phase problems via Morse theory. Commun. Contemp. Math. 20(2), 1750023, 14 (2018)MathSciNetCrossRef
115.
V.D. Rădulescu, D.D. Repovš, Partial Differential Equations with Variable Exponents. Monographs and Research Notes in Mathematics (CRC Press, Boca Raton, FL, 2015). Variational methods and qualitative analysis
119.
123.
Y. Sawano, T. Shimomura, Sobolev embeddings for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces over non-doubling measure spaces. Integral Transforms Spec. Funct. 25(12), 976–991 (2014)MathSciNetCrossRef
128.
Q. Zhang, V.D. Rădulescu, Double phase anisotropic variational problems and combined effects of reaction and absorption terms. J. Math. Pures Appl. (9) 118, 159–203 (2018)MathSciNetCrossRef
129.
V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory. Math. USSR-Izv. 29, 675–710, 877 (1987)CrossRef
Metadaten
Titel
Special Cases
verfasst von
Petteri Harjulehto
Peter Hästö
Copyright-Jahr
2019
Buch
Orlicz Spaces and Generalized Orlicz Spaces

Print ISBN: 978-3-030-15099-0

Electronic ISBN: 978-3-030-15100-3

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-030-15100-3_7