Hölder condition

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Hölder condition

[′hel·dər kən‚dish·ən]
(mathematics)
A function ƒ(x) satisfies the Hölder condition in a neighborhood of a point x0 if |ƒ(x) - ƒ(x0)| ≤ c |(x-x0)| n , where c and n are constants.
A function ƒ(x) satisfies a Hölder condition in an interval or in a region of the plane if |ƒ(x) - ƒ(y)| ≤ c|x - y |nfor all x and y in the interval or region, where c and n are constants.
References in periodicals archive ?
The case when f is of bounded variation and u Holder continuous
2] > 0, x [member of] [a, b], while the function u: [a, b] [right arrow] R satisfies some local Holder continuous, namely,
The case when f is absolutely continuous and u Holder continuous
T] (S) we denote the spaces of Holder continuous functions and Holder continuous tangential fields (0 < [alpha] < 1), respectively.
The authors show that solutions of large classes of subelliptic equations with bounded measurable coefficients are Holder continuous.
X], which is Holder continuous with exponent [alpha] [member of] (0,1].
Then f is Holder continuous on [0,1] with Holder exponent 1/2:
7 The latter Lemma cannot be substantially improved, as in t = 1/4, the density f (t) is not Holder continuous with Holder exponent 1/2 + [member of] for any [member of] > 0.
Topics include a review of preliminaries such as continuous and Holder continuous functions, Sobolev spaces and convex analysis; classical methods such as Euler-Lagrange equations; direct methods such as the Dirichlet integral; regularity, such as the one-dimensinal case; minimal surfaces such as in the Douglas- Courant-Tonelli method; and isoperimetric inequality.