## Mathematics Subject Classification – MSC2020

History of partial differential equations [Consider also classification numbers pertaining to Section 01-XX] 383

Hamilton-Jacobi equations {For calculus of variations and optimal control, see 49Lxx; for mechanics of particles and systems, see 70H20} 791

Elliptic equations and elliptic systems {For global analysis, analysis on manifolds, see 58J10, 58J20} 83592

Monge-Ampère equations {For complex Monge-Ampère operators, see 32W20; for parabolic Monge-Ampère equations, see 35K96} 480

Parabolic equations and parabolic systems {For global analysis, analysis on manifolds, see 58J35} 63766

Overdetermined problems for partial differential equations and systems of partial differential equations {For global analysis, see 58Hxx, 58J10, 58J15} 1831

Spectral theory and eigenvalue problems for partial differential equations {For operator theory, see 47Axx, 47Bxx, 47F05} 20520

Time-dependent Schrödinger equations and Dirac equations {For quantum theory, see 81Q05; for relativity and gravitational theory, see 83A05, 83C10} 1853

KdV equations (Korteweg-de Vries equations) {For dynamical systems and ergodic theory, see 37K10} 16868

NLS equations (nonlinear Schrödinger equations) {For dynamical systems and ergodic theory, see 37K10} 13160

Maxwell equations {For optics and electromagnetic theory, see 78A25; for relativity and gravitational theory, see 83C22} 1214

Fokker-Planck equations {For fluid mechanics, see 76X05, 76W05; for statistical mechanics, see 82C31} 1130

PDEs in connection with mean field game theory {For calculus of variations and optimal control, see 49N80; for game theory, see 91A16} 12

Pseudodifferential operators and other generalizations of partial differential operators {For operator theory, see 47G30, 58J40} 6497