Regularity Techniques for Elliptic PDEs and the Fractional Laplacian

Pablo Raúl Stinga

Jul 2024 · CRC Press

About this eBook

Regularity Techniques for Elliptic PDEs and the Fractional Laplacian 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. The emphasis is placed on ideas and the development of intuition, while at the same time being completely rigorous. The reader should keep in mind that this text is about how analysis can be applied to regularity estimates. Many methods are nonlinear in nature, but the focus is on linear equations without lower order terms, thus avoiding bulky computations. The philosophy underpinning the book is that ideas must be flushed out in the cleanest and simplest ways, showing all the details and always maintaining rigor.

Features

• Self-contained treatment of the topic
• Bridges the gap between upper undergraduate textbooks and advanced monographs to offer a useful, accessible reference for students and researchers.
• Replete with useful references.

About the author

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 Autόnoma 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.