Mathematical Sciences Classification System

58Jxx - Partial differential equations on manifolds; differential operators
[See also 32Wxx, 35-XX, 53Cxx]

  • 9
    58J05
    Elliptic equations on manifolds, general theory [See also 35-XX]
  • 1
    58J10
    Differential complexes [See also 35Nxx]; elliptic complexes
  • 1
    58J15
    Relations with hyperfunctions
  • 14
    58J20
    Index theory and related fixed point theorems [See also 19K56, 46L80]
  • 58J22
    Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
  • 58J26
    Elliptic genera
  • 5
    58J28
    Eta-invariants, Chern-Simons invariants
  • 1
    58J30
    Spectral flows
  • 9
    58J32
    Boundary value problems on manifolds
  • 26
    58J35
    Heat and other parabolic equation methods
  • 1
    58J37
    Perturbations; asymptotics
  • 22
    58J40
    Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]
  • 6
    58J42
    Noncommutative global analysis, noncommutative residues
  • 12
    58J45
    Hyperbolic equations [See also 35Lxx]
  • 58J47
    Propagation of singularities; initial value problems
  • 23
    58J50
    Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
  • 3
    58J51
    Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
  • 3
    58J52
    Determinants and determinant bundles, analytic torsion
  • 58J53
    Isospectrality
  • 58J55
    Bifurcation [See also 35B32]
  • 3
    58J60
    Relations with special manifold structures (Riemannian, Finsler, etc.)
  • 16
    58J65
    Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
  • 7
    58J70
    Invariance and symmetry properties [See also 35A30]
  • 5
    58J72
    Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]
  • 58J90
    Applications
  • 1
    58J99
    None of the above, but in this section

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