Note on Regularity theory for Nonlinear elliptic equations
Zhenye Qian
TL;DR
This paper reviews key developments in the regularity theory of nonlinear elliptic equations, covering classical and modern approaches to understanding solution smoothness and behavior.
Contribution
It summarizes seminal theories and advances in regularity results for nonlinear elliptic equations, highlighting the evolution of the field.
Findings
De Giorgi-Nash-Moser theory for Hilbert 19th problem
Krylov-Safonov and Evans-Safonov theories for fully nonlinear equations
Comprehensive overview of regularity results in nonlinear elliptic PDEs
Abstract
In this note, we present several seminal developments in the regularity theory of nonlinear (uniformly) elliptic equations, including the De Giorgi-Nash-Moser theory concerning the Hilbert 19th problem and variational equations, as well as the Krylov-Safonov and Evans-Safonov theories for fully nonlinear equations.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Algebraic and Geometric Analysis · Mathematical and Theoretical Analysis