Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics

Autor: Michael Hinz, Anna Rozanova-Pierrat, Alexander Teplyaev

Publikováno v: SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2021, 59 (2), pp.1007-1032. ⟨10.1137/20M1361687⟩

We introduce new parametrized classes of shape admissible domains in R^n , n $\ge$ 2, and prove that they are compact with respect to the convergence in the sense of characteristic functions, the Hausdorff sense, the sense of compacts and the weak co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::295de314736a182a619ec8a727ead5b3
https://doi.org/10.1137/20m1361687

Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates

Autor: Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev

Publikováno v: Calculus of Variations and Partial Differential Equations. 60

With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Dirichlet spaces with a heat kernel satisfying sub-Gaussian estimates. U

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43335316d98bc84486e3495216019729
https://doi.org/10.1007/s00526-021-02041-2

Spectral decimation of a self-similar version of almost Mathieu-type operators

Autor: Gamal Mograby, Radhakrishnan Balu, Alexander Teplyaev, Kasso Okoudjou

We introduce self-similar versions of the one-dimensional almost Mathieu operators. Our definition is based on a class of self-similar Laplacians instead of the standard discrete Laplacian, and includes the classical almost Mathieu operators as a par

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b91f9a18cf550247f43a06baf8c2617
http://arxiv.org/abs/2105.09896

From Classical Analysis to Analysis on Fractals : A Tribute to Robert Strichartz, Volume 1

Autor: Patricia Alonso Ruiz, Michael Hinz, Kasso A. Okoudjou, Luke G. Rogers, Alexander Teplyaev

Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis

Analysis, Probability and Mathematical Physics on Fractals

Autor: Luke G. Rogers, Joe P. Chen, Alexander Teplyaev, Robert S. Strichartz, Patricia Alonso Ruiz

Publikováno v: Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications ISBN: 9789811215520
Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::873c96a620db9ed5278296ed1eb0a821
https://doi.org/10.1142/11696