Regularity Theory for Elliptic PDE

Abstract

This manuscript aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality. It can be seen as a bridge between an elementary PDE course and more advanced textbooks. This is a draft of the book "Regularity Theory for Elliptic PDE". The final version has been published in Zurich Lectures in Advanced Mathematics, EMS Press, 2022.

References in corpus (2)

• Pathological solutions to elliptic problems in divergence form with continuous coefficients
• Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D

Cited by in corpus (12)

• Integro-Differential Elliptic Equations
• The Multiscale Perturbation Method for Two-Phase Reservoir Flow Problems
• Schauder estimates for parabolic equations with degenerate or singular weights
• $C^{\infty }$ partial regularity of the singular set in the obstacle problem
• A quantitative study of radial symmetry for solutions to semilinear equations in ${\mathbb{R}}^n$
• Small scale creation for 2D free boundary Euler equations with surface tension
• Concavity and perturbed concavity for $p$-Laplace equations
• Why bootstrapping for $J$-holomorphic curves fails in $C^k$
• Improving the Regularity of Vector Fields
• Schauder estimates for flat solutions to a class of fully nonlinear elliptic PDEs with Dini continuous data: a geometric tangential approach
• Wild solutions to scalar Euler-Lagrange equations
• Notes on Schauder estimates by scaling for elliptic PDEs in divergence form