Zobrazeno 1 - 10
of 278
pro vyhledávání: '"A Rueland"'
We study the rigidity properties of the $T_3$-structure for the symmetrized gradient from \cite{BFJK94} qualitatively, quantitatively and numerically. More precisely, we complement the flexibility result for approximate solutions of the associated di
Externí odkaz:
http://arxiv.org/abs/2408.13110
We prove exponential instability properties for the fractional Calder\'on problem and the conductivity formulation of the fractional Calder\'on problem in the regime of fractional powers $s\in (0,1)$. We particularly focus on two settings: First, we
Externí odkaz:
http://arxiv.org/abs/2405.08381
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling law in the singular perturbation parameter. In these settings the resp
Externí odkaz:
http://arxiv.org/abs/2405.05927
Autor:
Rüland, Angkana
We revisit the source-to-solution anisotropic fractional Calder\'on problem introduced and analyzed in [FGKU21] and [F21]. Using the Caffarelli-Silvestre interpretation of the fractional Laplacian, we provide an alternative argument for the recovery
Externí odkaz:
http://arxiv.org/abs/2309.00858
We study the scaling behaviour of a class of compatible two-well problems for higher order, homogeneous linear differential operators. To this end, we first deduce general lower scaling bounds which are determined by the vanishing order of the symbol
Externí odkaz:
http://arxiv.org/abs/2306.14660
On the Scaling of the Cubic-to-Tetragonal Phase Transformation with Displacement Boundary Conditions
Autor:
Rüland, Angkana, Tribuzio, Antonio
We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustrate that the order of lamination of the affine displacement data deter
Externí odkaz:
http://arxiv.org/abs/2306.05740
We relate the (anisotropic) variable coefficient local and nonlocal Calder\'on problems by means of the Caffarelli-Silvestre extension. In particular, we prove that (partial) Dirichlet-to-Neumann data for the fractional Calder\'on problem in three an
Externí odkaz:
http://arxiv.org/abs/2305.04227
Autor:
Rüland, Angkana, Simon, Theresa M.
We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple laminates and crossing-twin structures can occur. In particular, we prove t
Externí odkaz:
http://arxiv.org/abs/2210.04304
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of $\mathcal{A}$-free operators and for a singularly perturbed $T_3$-structure for the divergence operator. In parti
Externí odkaz:
http://arxiv.org/abs/2209.09309
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154 (2024) 769-792
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed
Externí odkaz:
http://arxiv.org/abs/2207.13746