Zobrazeno 1 - 10
of 174
pro vyhledávání: '"31a25"'
Autor:
Nahon, Mickaël, Oudet, Édouard
We introduce a method to compute efficiently and with arbitrary precision a basis of harmonic functions with prescribed singularities on a general compact surface of genus two and more. This basis is obtained as a composition of theta functions and t
Externí odkaz:
http://arxiv.org/abs/2410.06763
Autor:
Lee, Haesung
In this paper, we study the Dirichlet problem for Laplace's equation in an open disk. The uniqueness of solutions is ensured by the well-known weak maximum principle. We introduce a novel approach to demonstrate the existence of a solution using harm
Externí odkaz:
http://arxiv.org/abs/2407.01197
We study the $\bar\partial$ equation subject to various boundary value conditions on bounded simply connected Lipschitz domains $D\subset\mathbb C$: for the Dirichlet problem with datum in $L^p(bD, \sigma)$, this is simply a restatement of the fact t
Externí odkaz:
http://arxiv.org/abs/2402.06747
We give new characterizations of the optimal data space for the $L^p(bD,\sigma)$-Neumann boundary value problem for the $\bar{\partial}$ operator associated to a bounded, Lipschitz domain $D\subset\mathbb{C}$. We show that the solution space is embed
Externí odkaz:
http://arxiv.org/abs/2402.05670
In this paper, we study the recovery of multi-layer structures in inverse conductivity problem by using one measurement. First, we define the concept of Generalized Polarization Tensors (GPTs) for multi-layered medium and show some important properti
Externí odkaz:
http://arxiv.org/abs/2312.02421
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whose derivative is analytic and a finite sum of terms involving the logar
Externí odkaz:
http://arxiv.org/abs/2309.12459
Autor:
Nessmann, Andreas
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel method to com
Externí odkaz:
http://arxiv.org/abs/2212.07258
Publikováno v:
J. Math. Phys., 63, Paper No. 063303, 2022
We investigate the phase diagram of the complex cubic unitary ensemble of random matrices with the potential $V(M)=-\frac{1}{3}M^3+tM$ where $t$ is a complex parameter. As proven in our previous paper, the whole phase space of the model, $t\in\mathbb
Externí odkaz:
http://arxiv.org/abs/2201.12871
Autor:
Bennetts, Luke G., Peter, Malte A.
Extensions of Rayleigh-Bloch waves above the cut-off frequency are studied via the discrete spectrum of a transfer operator for a generalised channel containing a single cylinder. Their wavenumbers are shown to become complex-valued and an additional
Externí odkaz:
http://arxiv.org/abs/2201.05295
In this article, first we give a general lemma on the existence of regular homeomorphic solutions $f$ with the hydrodynamic normalization $f(z)=z+o(1)$ as $z\to\infty$ to the degenerate Beltrami equations $\overline{\partial}f=\mu\,\partial f$ in $\m
Externí odkaz:
http://arxiv.org/abs/2111.10375