Orlicz Spaces and Generalized Orlicz Spaces

By Petteri Harjulehto, P. Hasto. Lecture notes in mathematics, 2019

542 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/64c786f5c8eca2ee769238eae9b1cbb01bde9c55

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Citations in the corpus

Local Hölder continuity for fractional nonlocal equations with general growth (2021, background): “For more examples of g and applications of problems with general growth, we refer to [3, 27, 46].”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, unknown): “These results are mainly taken from Crespo-BlancoGasiński-Harjulehto-Winkert [16], we refer also to the books of Diening-Harjulehto-Hästö-Růžička [27], Harjulehto-Hästö [37], Musielak [56], Rădulescu-Repovš [61] and the papers of Colasuonno-Squassina [15], Fan [29], Fan-Zhao [30], Kováčik-Rákosńık [”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “Next, we want to check the relation between the modular ρH and its norm ‖ · ‖H, see also Harjulehto-Hästö [41].”
Uniqueness (2021, unknown): “For an introduction to Orlicz spaces we refer to [24, 27, 30, 22]; we extensively used some optimal”
On the Regularity of Minima of Non-autonomous Functionals (2019, background): “For this we refer to [36–39, 50].”
Manifold Constrained Non-uniformly Elliptic Problems (2019, background): “ naturally deﬁned on Musielak-Orlicz-Sobolev spaces/classes W1,Φ, i.e., W1,Φ(Ω,RN) = n f ∈ W1,1(Ω,RN) : Φ(·,|f|) +Φ(·,|Df|) ∈ L1(Ω) o . (1.9) Forsuch spaces werefer to therecent interesting monograph [34]. Amainproblem here isthe oneofﬁnding general conditions ensuring the regularity of minimizers. ”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, result): “We refer to Colasuonno–Squassina [13], Harjulehto–Hästö [31] and Musielak [41] for the main results in this direction.”
Lipschitz Bounds and Nonautonomous Integrals (2020, background): “Connections to related function spaces have been studied too [27, 49, 63].”
Maximal regularity for local minimizers of non-autonomous functionals (2019, methodology): “Note that this version of (A0) is slightly stronger than the one used in [51], but they are equivalent under the doubling assumption (aDec).”