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"Elliptic equations" as a book category denotes works centered on elliptic partial differential equations—typically second‑order (but also higher‑order) linear and nonlinear operators whose principal symbol is positive definite—treating existence, uniqueness, regularity, and qualitative behavior of solutions to boundary value problems such as Laplace's and Poisson's equations, the Helmholtz and Stokes problems, and nonlinear examples like the p‑Laplace and Monge–Ampère equations. Titles in this category range from introductory texts that develop harmonic functions, maximum principles, Sobolev spaces, and weak formulations to advanced monographs on Schauder and Calderón–Zygmund estimates, spectral theory, elliptic regularity, variational methods, and nonlinear analysis, as well as computational and applied works addressing numerical schemes and applications in geometry, physics, materials science, and probability.

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