Donatella Danielli

About

Donatella Danielli is a professor of Mathematics and the director of the School of Mathematical and Statistical Sciences at Arizona State University (ASU). She leads faculty, instructors, and lecturers that teach mathematics to over 23,000 students annually across various disciplines. Her responsibilities include overseeing degree and research programs in theoretical mathematics, applied mathematics, mathematics education, statistics and data science, as well as actuarial science. Danielli is dedicated to promoting excellence in research and teaching within the school and strives to create a more equitable and inclusive academic environment for students, faculty, and staff. Prior to her appointment at ASU in January 2021, Danielli was a professor of Mathematics at Purdue University, where she received her doctorate in mathematics in 1999. Her research focuses on the study of analytic and geometric properties of partial differential equations and variational inequalities, with recent interests in lower dimensional obstacle problems and free boundary problems related to flame propagation. She has been recognized with numerous honors, including being named a Fellow of the American Mathematical Society and the Association for Women in Mathematics, and has received grants such as an NSF CAREER Award. Danielli currently serves as co-editor-in-chief of La Matematica, the official journal of the Association for Women in Mathematics.

Research topics

• Computer Science
• Artificial Intelligence
• Applied mathematics
• Mathematical analysis
• Pure mathematics
• Algorithm
• Mathematics
• Combinatorics

Selected publications

• Geometric Properties of Solutions to Subelliptic Equations in Nilpotent Lie Groups

  CRC Press eBooks · 2020 · 17 citations

  1st authorCorresponding

  The aim of this paper is to establish some geometric properties of the level sets of solutions to sub-Laplacians in stratified, nilpotent Lie groups. Such properties are reminiscent of classical ones for harmonic functions, but the fact that they hold in the complex subelliptic geometry is a perhaps unexpected and interesting phenomenon. For the sake of simplicity we will focus on the capacitary problem, but similar ideas apply to more general situations and also, we hope, to nonlinear equations…

  PublisherDOI

• The structure of the singular set in the thin obstacle problem for degenerate parabolic equations

  Calculus of Variations and Partial Differential Equations · 2021-04-27 · 6 citations

  preprintOpen access

  Abstract We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight $$|y|^a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mo>|</mml:mo><mml:mi>y</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mi>a</mml:mi></mml:msup></mml:math> for $$a \in (-1,1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:mo>∈</mml:mo><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo>…

  PublisherOA PDFDOI

• On a weighted two-phase boundary obstacle problem

  Indiana University Mathematics Journal · 2023-01-01 · 2 citations

  article1st authorCorresponding

  In this work we consider an inhomogeneous two-phase obstacle-type problem driven by the fractional Laplacian. In particular, making use of the Caffarelli-Silvestre extension, Almgren- and Monneau-type monotonicity formulas, and blowup analysis, we provide a classification of the possible vanishing orders, which implies the strong unique continuation property. Moreover, we prove a stratification result for the nodal set, together with estimates on its Hausdorff dimensions, for both the regular an…

  PublisherDOI

• The obstacle problem for a higher order fractional Laplacian

  Calculus of Variations and Partial Differential Equations · 2023-08-23 · 2 citations

  article1st author
  PublisherDOI

• The obstacle problem for a higher order fractional Laplacian

  arXiv (Cornell University) · 2023-05-12 · 1 citations

  preprintOpen access1st authorCorresponding

  In this paper, we consider the obstacle problem for the fractional Laplace operator $(-Δ)^s$ in the Euclidian space $\mathbb{R}^n$ in the case where $1

  PublisherOA PDFDOI

Recent grants

• CAREER: Analytic and Geometric Aspects of Partial Differential Equations

  NSF · $400k · 2003–2010

• Analysis and Geometry of Nonlinear PDEs

  NSF · $238k · 2008–2014

• Analytic and geometric properties of variational inequalities and PDE

  NSF · $225k · 2011–2016

Frequent coauthors

• Nicola Garofalo

  49 shared

• Arshak Petrosyan

  22 shared

• Duy-Minh Nhieu

  National Central University

  17 shared

• Scott D. Pauls

  Dartmouth College

  7 shared

• Agnid Banerjee

  Tata Institute of Fundamental Research

  7 shared

• Camelia A. Pop

  University of Minnesota

  7 shared

• Luca Capogna

  6 shared

• Alaa Haj Ali

  6 shared

Education

• Ph.D., Mathematics

  Purdue University

  1999

• Other

  University of Bologna

  1989

Awards & honors

• 2020 Fellow of the Association for Women in Mathematics
• 2018-19 Fellow of the Big Ten Academic Alliance Academic Lea…
• 2018 Purdue Book of Great Teachers inductee
• 2017 Fellow of the American Mathematical Society
• 2014 Simons Foundation Fellow in Mathematics

Similar researchers at Arizona State University

• Hal Kiersteadh-34
• Zdzislaw Jackiewiczh-33
• Sharon Crookh-23