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pro vyhledávání: '"ZÄHLE, MARTINA"'
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider mean values of the Lipschitz-Killing curvatures of their parallel sets
Externí odkaz:
http://arxiv.org/abs/2107.14431
Autor:
Issoglio, Elena, Zähle, Martina
Publikováno v:
Stochastic Partial Differential Equations: Analysis and Computations, June 2015, Volume 3, Issue 2, pp 272-289
In this paper we study the regularity of non-linear parabolic PDEs and stochastic PDEs on metric measure spaces admitting heat kernels. In particular we consider mild function solutions to abstract Cauchy problems and show that the unique solution is
Externí odkaz:
http://arxiv.org/abs/1409.3399
Autor:
Rataj, Jan, Zähle, Martina
Publikováno v:
J. Geom. Anal. 25 (2015) 2133-2147
Properties of general Legendrian cycles $T$ acting in ${\mathbb R}^d\times S^{d-1}$ are studied. In particular, we give short proofs for certain uniqueness theorems with respect to the projections on the first and second component of such currents: I
Externí odkaz:
http://arxiv.org/abs/1402.2249
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random situations, they pr
Externí odkaz:
http://arxiv.org/abs/1312.3272
Autor:
Radchenko, Vadym, Zähle, Martina
Publikováno v:
Statistics and Probability Letters, 82 (2012), 699-704
A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is less than 4/
Externí odkaz:
http://arxiv.org/abs/1208.0445
Autor:
Bohl, Tilman Johannes, Zähle, Martina
Publikováno v:
Geometriae Dedicata 2012
We obtain fractal Lipschitz-Killing curvature-direction measures for a large class of self-similar sets F in R^d. Such measures jointly describe the distribution of normal vectors and localize curvature by analogues of the higher order mean curvature
Externí odkaz:
http://arxiv.org/abs/1111.4457
Autor:
Rataj, Jan, Zähle, Martina
For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated fractal cur
Externí odkaz:
http://arxiv.org/abs/1009.6162
Autor:
Zähle, Martina
For a large class of self-similar random sets F in R^d geometric parameters C_k(F), k=0,...,d, are introduced. They arise as a.s. (average or essential) limits of the volume C_d(F(\epsilon)), the surface area C_{d-1}(F(\epsilon)) and the integrals of
Externí odkaz:
http://arxiv.org/abs/1009.6166
Autor:
Winter, Steffen, Zähle, Martina
Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures C_k(F_r,.)
Externí odkaz:
http://arxiv.org/abs/1007.0696
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