arXiv subjects

A. Zimmermann

Publications and source records attributed to A. Zimmermann.

3 recordsLinked to original sources

arXiv2026

The Neumann problem for a multivalued p-Laplace equation of Allen-Cahn type with a multiplicative stochastic force

In this paper, we consider a parabolic problem with constraint written as a differential inclusion, driven by a multiplicative colored noise and involving a p-Laplace operator (for $p \geq 2$), nonlinear random source terms and subject to Neumann boundary conditions on a bounded Lipschitz domain of $R^d$ with $d \geq 1$. This contribution aims at proving existence and uniqueness of a solution for such a multivalued problem. On one hand, the existence result is proved by the analysis of a semi-implicit time discretization scheme constructed on a smoother version of our problem, itself obtained by a regularization "\`a la Moreau-Yosida" of the subdifferential term. The key point of our approach consists in finding a clever relation between the time step denoted $\tau$ and the Moreau-Yosida regularization parameter denoted $\epsilon$ in view to pass simultaneously to the limit with respect to $\tau$ and $\epsilon$. On the other hand, the uniqueness of the solution is proved by standard arguments.

math.AP↗

arXiv2020

Entropy solutions of doubly nonlinear fractional Laplace equations

In this contribution, we study a class of doubly nonlinear elliptic equations with bounded, merely integrable right-hand side on the whole space $\mathbb{R}^N$. The equation is driven by the fractional Laplacian $(-Δ)^{\frac{s}{2}}$ for $s\in (0,1]$ and a strongly continuous nonlinear perturbation of first order. It is well known that weak solutions are in genreral not unique in this setting. We are able to prove an $L^1$-contraction and comparison principle and to show existence and uniqueness of entropy solutions.

math.AP↗

arXiv2016

The iridium double perovskite Sr2YIrO6 revisited: A combined structural and specific heat study

Recently, the iridate double perovskite Sr$_2$YIrO$_6$ has attracted considerable attention due to the report of unexpected magnetism in this Ir$^{5+}$ (5d$^4$) material, in which according to the J$_{eff}$ model, a non-magnetic ground state is expected. However, in recent works on polycrystalline samples of the series Ba$_{2-x}$Sr$_x$YIrO$_6$ no indication of magnetic transitions have been found. We present a structural, magnetic and thermodynamic characterization of Sr$_2$YIrO$_6$ single crystals, with emphasis on the temperature and magnetic field dependence of the specific heat. Here, we demonstrate the clue role of single crystal X-ray diffraction on the structural characterization of the Sr$_2$YIrO$_6$ double perovskite crystals by reporting the detection of a $\sqrt{2}a \times \sqrt{2}a \times 1c$ supercell, where $a$, $b$ and $c$ are the unit cell dimensions of the reported monoclinic subcell. In agreement with the expected non-magnetic ground state of Ir$^{5+}$ (5d$^4$) in Sr$_2$YIrO$_6$, no magnetic transition is observed down to 430~mK. Moreover, our results suggest that the low temperature anomaly observed in the specific heat is not related to the onset of long-range magnetic order. Instead, it is identified as a Schottky anomaly caused by paramagnetic impurities present in the sample, of the order of $n \sim 0.5(2)$ \%. These impurities lead to non-negligible spin correlations, which nonetheless, are not associated with long-range magnetic ordering.

cond-mat.mtrl-sci↗