## Mathematics Subject Classification – MSC2020

History of partial differential equations [Consider also classification numbers pertaining to Section 01-XX] 390

Hamilton-Jacobi equations {For calculus of variations and optimal control, see 49Lxx; for mechanics of particles and systems, see 70H20} 845

Elliptic equations and elliptic systems {For global analysis, analysis on manifolds, see 58J10, 58J20} 85119

Monge-Ampère equations {For complex Monge-Ampère operators, see 32W20; for parabolic Monge-Ampère equations, see 35K96} 512

Parabolic equations and parabolic systems {For global analysis, analysis on manifolds, see 58J35} 65062

Overdetermined problems for partial differential equations and systems of partial differential equations {For global analysis, see 58Hxx, 58J10, 58J15} 1852

Spectral theory and eigenvalue problems for partial differential equations {For operator theory, see 47Axx, 47Bxx, 47F05} 20843

Time-dependent Schrödinger equations and Dirac equations {For quantum theory, see 81Q05; for relativity and gravitational theory, see 83A05, 83C10} 1949

KdV equations (Korteweg-de Vries equations) {For dynamical systems and ergodic theory, see 37K10} 17170

NLS equations (nonlinear Schrödinger equations) {For dynamical systems and ergodic theory, see 37K10} 13480

Maxwell equations {For optics and electromagnetic theory, see 78A25; for relativity and gravitational theory, see 83C22} 1269

Fokker-Planck equations {For fluid mechanics, see 76X05, 76W05; for statistical mechanics, see 82C31} 1197

PDEs in connection with mean field game theory {For calculus of variations and optimal control, see 49N80; for game theory, see 91A16} 14

Pseudodifferential operators and other generalizations of partial differential operators {For operator theory, see 47G30, 58J40} 6580