A Generalized Version of the Lions-Type Lemma
نویسندگان
چکیده
Abstract In this short paper, I recall the history of dealing with lack compactness a sequence in case an unbounded domain and prove vanishing Lions-type result for Lebesgue-measurable functions. This lemma generalizes some results class Orlicz–Sobolev spaces. What matters here is behavior integral, not space.
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Lasry-Lions regularization and a Lemma of Ilmanen
inf u 6 Ttu(x) 6 u(x) 6 Ťtu(x) 6 supu for each t > 0 and each x ∈ H. A function u : H −→ R is called k-semi-concave, k > 0, if the function x −→ u(x)−‖x‖2/k is concave. The function u is called k-semi-convex if −u is k-semiconcave. A bounded function u is t-semi-concave if and only if it belongs to the image of the operator Tt, this follows from Lemma 1 and Lemma 3 below. A function is called s...
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ژورنال
عنوان ژورنال: Annales Mathematicae Silesianae
سال: 2023
ISSN: ['0860-2107', '2391-4238']
DOI: https://doi.org/10.2478/amsil-2023-0014