Juan J. Manfredi

Juan J. Manfredi is a Professor of Mathematics at the University of Pittsburgh's Department of Mathematics, part of the Dietrich School of Arts and Sciences. He holds a PhD from Washington University in St. Louis, focusing on quasiregular mappings and partial differential equations. His research emphasizes elliptic and parabolic PDEs of p-Laplacian type, sub-Riemannian manifolds, and game-theoretic interpretations of equations like the infinity Laplacian. He explores regularity properties of p-harmonic functions and their applications in stochastic processes and signal processing.

His work spans nonlinear potential theory, subelliptic equations, and geometric analysis. Notable contributions include studies on Monge-Ampère equations, viscosity solutions, and the interplay between stochastic games (e.g., tug-of-war) and PDEs. He has collaborated on topics like Carnot groups, Heisenberg group geometry, and Riemannian approximations in sub-Riemannian settings.

Recent publications highlight advancements in asymptotic mean-value formulas, BMO estimates for solutions, and convergence principles for dynamic programming. His research bridges pure analysis and applied problems, including mass transport and optimal control. While no formal awards are listed, his extensive bibliography and academic roles reflect significant scholarly impact.

Manfredi maintains an active online presence with resources like the QuasiWorld page, offering lecture notes and computational tools. His work often intersects with probability, geometric analysis, and numerical methods, positioning him at the forefront of modern nonlinear PDE research.