"This book presents the proceedings of the international workshop, "Advances in Mathematical Analysis of Partial Differential Equations" held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations."--Back cover.

Includes bibliographical references.

On singular parabolic Laplacian systems under nonsmooth external forces. Regularity up to the boundary;On the fundamental matrix solution for higher-order parabolic systems;On variational ground of the Hessian operators;The magneto-geostrophic equations: a survey;Variations on Liouville's theorem in the setting of stationary flows of generalized Newtonian fluids in the plane;On the normal-type parabolic system corresponding to the three-dimensional Helmholtz system;A discrete Bernoulli free boundary problem;On Plateau's problem in Riemannian manifolds;The boundary Harnack principle for second order elliptic equations in John and uniform domains;Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients;Singular solutions of Navier-Stokes equations;The local regularity theory for the Navier-Stokes equations near the boundary; _p theory of free boundary problems of magnetohydrodynamics in simply connected domains