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Dariush Ehsani

Publications and source records attributed to Dariush Ehsani.

At least 19 recordsLinked to original sources
arXiv2024

An Overview of zbMATH Open Digital Library

Mathematical research thrives on the effective dissemination and discovery of knowledge. zbMATH Open has emerged as a pivotal platform in this landscape, offering a comprehensive repository of mathematical literature. Beyond indexing and abstracting, it serves as a unified quality-assured infrastructure for finding, evaluating, and connecting mathematical information that advances mathematical research as well as interdisciplinary exploration. zbMATH Open enables scientific quality control by post-publication reviews and promotes connections between researchers, institutions, and research outputs. This paper represents the functionalities of the most significant features of this open-access service, highlighting its role in shaping the future of mathematical information retrieval.

cs.DL↗
arXiv2022

Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities

We obtain subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces embedded in $\mathbb{C}^n$ with isolated singularities. $W^ε$ Sobolev norms of a form, $f$, for $0< ε< 1$ are estimated in terms of weighted $L^2$ norms of $\bar{\partial} f$ and $\bar{\partial}^{\ast}f$, with weights which vanish at the singularities, as well as weighted $L^2$ norms of $f$, with weights which blow up at the singularities.

math.CV↗
arXiv2021

zbMATH Open: API Solutions and Research Challenges

We present zbMATH Open, the most comprehensive collection of reviews and bibliographic metadata of scholarly literature in mathematics. Besides our website https://zbMATH.org which is openly accessible since the beginning of this year, we provide API endpoints to offer our data. The API improves interoperability with others, i.e., digital libraries, and allows using our data for research purposes. In this article, we (1) illustrate the current and future overview of the services offered by zbMATH; (2) present the initial version of the zbMATH links API; (3) analyze potentials and limitations of the links API based on the example of the NIST Digital Library of Mathematical Functions; (4) and finally, present the zbMATH Open dataset as a research resource and discuss connected open research problems.

cs.DL↗
arXiv2018

Exact regularity of the $\bar{\partial}$-problem with dependence on the $\bar{\partial}_b$-problem on weakly pseudoconvex domains in $\mathbb{C}^2$

We reduce the problem of constructing a linear solution operator to the $\bar{\partial}$-equation on smoothly bounded weakly pseudoconvex domains, $Ω$, in $\mathbb{C}^2$ to the problem of the boundary $\bar{\partial}_b$-equation. We show there is a solution operator to $\bar{\partial}$ which is bounded as a map $W^{s}_{(0,1)}(Ω)\cap{ker} \bar{\partial} \rightarrow W^{s}(Ω)$ for all $s\ge 0$ if there is a corresponding solution operator to the $\bar{\partial}_b$-problem with analogous regularity properties.

math.CV↗
arXiv2014

Regularity of dbar on worm domains

A solution operator to the $\bar{\partial}$-equation is constructed on unbounded worm domains, $D_β$. Regularity estimates are proven showing the operator preserves regularity of the data. The operator may be viewed as a continuous mapping among appropriate subpaces of $W^s(D_β)$, which depend on a rotational invariance of the domains.

math.CV↗
arXiv2009

Integral representations on non-smooth domains

We derive integral representations for $(0,q)$-forms, $q\ge1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains. A $(0,q)$-form, $f$ is written in terms of integral operators acting on $f$, $\mdbar f$, and $\mdbar^{\ast} f$. The representation is applied to derive $L^{\infty}$ estimates.

math.CV↗
arXiv2009

Weighted $C^k$ estimates for a class of integral operators on non-smooth domains

We apply integral representations for $(0,q)$-forms, $q\ge1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $C^k$ estimates for a given $(0,q)$-form, $f$, in terms of $C^k$ norms of $\mdbar f$, and $\mdbar^{\ast} f$. The weights are powers of the gradient of the defining function of the domain.

math.CV↗
arXiv2009

Boundary value problems on product domains

We consider the inhomogeneous Dirichlet problem on product domains. The main result is the asymptotic expansion of the solution in terms of increasing smoothness up to the boundary. In particular, we show the exact nature of the singularities of the solution at singularities of the boundary by constructing singular functions which make up an asymptotic expansion of the solution.

math.AP↗