Joel Spruck (born 1946[1]) is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations.
With Basilis Gidas, Spruck studied positive solutions of subcritical second-order elliptic partial differential equations of Yamabe type.
With Caffarelli, they studied the Yamabe equation on Euclidean space, proving a positive mass-style theorem on the asymptotic behavior of isolated singularities.
In 1974, Spruck and David Hoffman extended a mean curvature-based Sobolev inequality of James H. Michael and Leon Simon to the setting of submanifolds of Riemannian manifolds.
[8] The works of Evans–Spruck and Chen–Giga–Goto found significant application in Gerhard Huisken and Tom Ilmanen's solution of the Riemannian Penrose inequality of general relativity and differential geometry, where they adopted the level-set approach to the inverse mean curvature flow.