Pablo Raúl Stinga
Iowa State University, IA·Mathematics & Statistics
Many real-world problems come down to equations about shapes and about how things influence each other across distances. Designers of ship hulls and car bodies, and image-repair software, rely on 'surfaces of minimum mean curvature variation.' These are surfaces bent as smoothly as possible.
- Fields
Mathematics & Statistics
- Topics
partial differential equations
elliptic equations
fractional Laplacian
- Grants
- 1 known grant, through Aug 2029
What they work on
- Establish the analytical theory of surfaces of minimum mean curvature variation, smoothly bending surfaces used in data interpolation, image repair and hull design, including well-posedness and regularity of their equations.
- Create a robust, transferable method for imposing nonhomogeneous boundary conditions on nonlocal equations, which model long-range interactions, in bounded domains, using tools from functional analysis and PDE theory.
- Prove regularity estimates for local and nonlocal transmission problems with a fixed interface, which arise in fibered materials and long-range interaction models, using geometric analysis and the calculus of variations.
More about the research
Models in climate science, plasma physics, population dynamics, disease spread and social media are often 'nonlocal.' In a nonlocal model, events far away instantly affect the system here. These systems often have sharp boundaries or interfaces, such as the beach separating ocean-surface and land-surface temperatures. This project builds the mathematical foundations these models need.
Why it matters
Algorithms for surface design, image reconstruction and data interpolation, and computer models of climate, population growth and disease spread, all depend on equations whose basic behavior is not fully understood. By proving when solutions exist and how smooth they are, and how to handle boundaries in nonlocal models, this work could support more efficient and reliable computational and artificial intelligence methods in these areas.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Hung Tran
University of Wisconsin-Madison, WI·Mathematics & Statistics
Establish regularity and large-time behavior results for Hamilton-Jacobi equations, a class of nonlinear PDE from optimal control, and use them to prove that mass-conserving solutions of critical coagulation-fragmentation equations exist.
Dionyssios Mantzavinos
University of Kansas, KS·Mathematics & Statistics
Develop analytical tools to establish existence, uniqueness and stability of solutions to nonlinear partial differential equations posed in bounded domains in two or more spatial dimensions.
William Minicozzi
Massachusetts Institute of Technology, MA·Mathematics & Statistics
Establish gradient estimates and monotonicity formulas for harmonic functions and heat equation solutions, clarifying how they depend on dimension and how elliptic and parabolic behavior relate.
The school
Iowa State University: 23 labs on PI Pages, $462M a year on research, 327 research doctorates a year.
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