scholarly journals ON THE REGULARITY OF SLE TRACE

2017 ◽  
Vol 5 ◽  
Author(s):  
PETER K. FRIZ ◽  
HUY TRAN
Keyword(s):  
Half Space ◽  
Embedding Theorem ◽  
Hölder Regularity ◽  
Besov Regularity ◽  
Holder Regularity ◽  
Space Capacity ◽  
Finite Moments ◽  
Optimal Variation

We revisit regularity of SLE trace, for all $\unicode[STIX]{x1D705}\neq 8$, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index $\min (1+\unicode[STIX]{x1D705}/8,2)$, improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

scholarly journals Hölder regularity for the spectrum of translation flows

2021 ◽  
Vol 8 ◽  
pp. 279-310
Author(s):  
Alexander I. Bufetov ◽  
Boris Solomyak
Keyword(s):  
Hölder Regularity ◽  
Holder Regularity

PATH PROPERTIES OF THE LINEAR MULTIFRACTIONAL STABLE MOTION

Fractals ◽  
2005 ◽  
Vol 13 (02) ◽  
pp. 157-178 ◽  
Author(s):  
STILIAN STOEV ◽  
MURAD S. TAQQU
Keyword(s):  
Heavy Tails ◽  
Hölder Regularity ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Stable Motion ◽  
Multifractional Brownian Motion ◽  
Sample Paths ◽  
Hölder Exponents ◽  
Fractional Stable Motion ◽  
Holder Regularity

The linear multifractional stable motion (LMSM) processes Y = {Y(t)}t∈ℝ is an α-stable (0 < α < 2) stochastic process, which exhibits local self-similarity, has heavy tails and can have skewed distributions. The process Y is obtained from the well-known class of linear fractional stable motion (LFSM) processes by replacing their self-similarity parameter H by a function of time H(t). We show that the paths of Y(t) are bounded on bounded intervals only if 1/α ≤ H(t) < 1, t ∈ ℝ. In particular, if 0 < α ≤ 1, then Y has everywhere discontinuous paths, with probability one. On the other hand, Y has a version with continuous paths if H(t) is sufficiently regular and 1/α < H(t), t ∈ ℝ. We study the Hölder regularity of the sample paths when these are continuous and establish almost sure bounds on the pointwise and uniform pointwise Hölder exponents of the (random) function Y(t,ω), t ∈ ℝ, in terms of the function H(t) and its corresponding Hölder exponents. The Gaussian multifractional Brownian motion (MBM) processes are LMSM processes when α = 2. We obtain some new results on the Hölder regularity of their paths.

Sign in / Sign up

Export Citation Format

Share Document