This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school "Geometric Measure Theory and Applications - From Geometric Analysis to Free Boundary Problems" which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro.

Providing an up-to-date account of the Yau conjecture, a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves, it will be of interest to students and researchers in mathematical analysis and its applications.

Inhalt

• Introduction. - A-Free Measures and Applications. - Regularity of Free Boundaries in Obstacle Problems. - Bernoulli Type Free Boundary Problems and Water Waves.