Elliptic PDE
Laplace, Poisson, and second-order elliptic equations; regularity theory.
Elliptic PDE. Laplace, Poisson, and second-order elliptic equations; regularity theory.
Foundations and canonical references
The standard treatments of elliptic pde approach the subject from complementary angles. Gilbarg, Elliptic Partial Differential Equations of Second Order (2001) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Evans, Partial Differential Equations (2010) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for elliptic pde include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2001Elliptic Partial Differential Equations of Second Ordergilbarg-2001, trudinger-2001
- textbook · primary · 2010Partial Differential Equationsevans-2010
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Review this topic
This page was drafted by an agent and is waiting on expert review. Spotted a wrong prerequisite, a missing concept, a misattributed source, or a factual slip? Tell us — your review opens a tracked issue maintainers act on.