Regularity Techniques for Elliptic PDEs and the Fractional Laplacian

This book presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian.

Autorentext

Pablo Raúl Stinga earned his Licenciatura en Ciencias Matemáticas degree at Universidad Nacional de San Luis, in San Luis, Argentina (2005). He earned his Máster en Matemáticas y Aplicaciones (2007), and his Doctorado en Matemáticas Doctor Europeus under the direction of José L.Torrea at Universidad Aut noma de Madrid, Spain (2010). He held postdoctoral research positions at Universidad de Zaragoza, Spain (2010) and Universidad de La Rioja, Spain (2011-2012). During the period 2012-2015, he was the R.H. Bing Fellow in Mathematics No.1 Instructor at the University of Texas at Austin, USA, where he worked as a postdoctoral researcher under the supervision of Luis A. Caffarelli. He is currently Associate Professor at Iowa State University, USA. His research interests are in analysis, partial differential equations and nonlocal fractional equations.