Mikhail Feldman

Mikhail Feldman is the Steenbock Professor of Mathematics at the University of Wisconsin–Madison, stationed in Van Vleck Hall. His work, continuously supported by the U.S. National Science Foundation, centers on nonlinear partial differential equations and their applications in fluid mechanics, optimal transport, and geometric analysis.

Research Interests

Feldman's core specialty lies in nonlinear PDEs, with particular depth in

• Transonic flow & shock waves – analyzing multidimensional transonic shocks, shock reflection-diffraction phenomena, and free-boundary problems arising from the compressible Euler equations.
• Optimal transport & Monge-Ampère equations – advancing the theory of Monge’s mass transport on Riemannian manifolds and its connection to semigeostrophic models in atmospheric science.
• Geometric evolution & free boundaries – studying regularity questions for free boundaries in fully nonlinear elliptic and parabolic problems.

Across these themes, his work integrates rigorous PDE analysis, geometric measure theory, and physical modeling, producing results on existence, uniqueness, stability, and regularity of solutions.

Publication Landscape

Over nearly three decades Feldman has authored or co-authored more than forty research articles. A clear temporal trend emerges: early contributions (1994-2002) focus on geometric PDEs and optimal transport, mid-career works (2003-2010) pivot to transonic shocks and free-boundary problems for the Euler equations, while recent papers (2011-2018) unify techniques from optimal transport with semigeostrophic fluid models. His collaborations with G.-Q. Chen, A. Tudorascu, M. Cullen, and others have produced influential studies published in leading journals such as Annals of Mathematics, Inventiones Mathematicae, and Archive for Rational Mechanics and Analysis.

Funding & Institutional Role

Feldman’s research has been supported by multiple National Science Foundation grants. At UW-Madison he holds the distinguished Steenbock endowed chair, underscoring his leadership role in the Department of Mathematics.

Laboratory & Collaborations

While no formal laboratory is listed, Feldman maintains active collaborations with researchers across North America and Europe, evidenced by frequent joint publications. His web page (https://people.math.wisc.edu/~feldman/) serves as the primary portal for preprints and lecture notes.