35-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations 70
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations 1256
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 3107
35-03 History of partial differential equations [Consider also classification numbers from Section 01-XX] 435
35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals 1296
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs [See also 32C38, 58J15] 1166
35A30 Geometric theory, characteristics, transformations in context of PDEs [See also 58J70, 58J72] 5147
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure [See also 74Q05, 74Q10, 76M50, 78M40, 80M40] 4981
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs [See also 37Cxx] 5286
35B32 Bifurcations in context of PDEs [See also 34C23, 34F10, 34H20, 37F46, 37Gxx, 37H20, 37J20, 37K50, 37L10, 37M20, 47J15, 58E05, 58E07, 58J55] 5357
35B35 Stability in context of PDEs [See also 34Dxx, 37B25, 37C20, 37C75, 37F15, 37J25, 37K45, 37L15, 49K40, 58K25, 93Dxx] 12671
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals) [See also 57R70, 58K05, 58E05] 1112
35Exx Partial differential equations and systems of partial differential equations with constant coefficients [See also 35N05] 2036
35Fxx General first-order partial differential equations and systems of first-order partial differential equations 7797
35F21 Hamilton-Jacobi equations {For calculus of variations and optimal control, see 49Lxx; for mechanics of particles and systems, see 70H20} 1271
35Gxx General higher-order partial differential equations and systems of higher-order partial differential equations 12917
35Jxx Elliptic equations and elliptic systems {For global analysis, analysis on manifolds, see 58J10, 58J20} 99464
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation [See also 31Axx, 31Bxx] 16667
35J10 Schrödinger operator, Schrödinger equation {For ordinary differential equations, see 34L40; for operator theory, see 47D08; for quantum theory, see 81Q05; for statistical mechanics, see 82B44} 8084
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators [See also 35R35, 49J40] 252
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators [See also 35R35, 49J40] 503
35J88 Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators [See also 35R35, 49J40] 71
35J96 Monge-Ampère equations {For complex Monge-Ampère operators, see 32W20; for parabolic Monge-Ampère equations, see 35K96} 841
35Kxx Parabolic equations and parabolic systems {For global analysis, analysis on manifolds, see 58J35} 76656
35K57 Reaction-diffusion equations {For diffusion processes and reaction effects, see 47D07, 58J65, 60J60, 60J70, 74N25, 76R50, 76V05, 80A23, 82B24, 82C24, 92E20} 16553
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 5571
35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 819
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators [See also 35R35, 49J40] 699
35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators [See also 35R35, 49J40] 302
35K87 Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators [See also 35R35, 49J40] 67
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators [See also 35R35, 49J40] 249
35L86 Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators [See also 35R35, 49J40] 56
35L87 Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators [See also 35R35, 49J40] 26
35Mxx Partial differential equations of mixed type and mixed-type systems of partial differential equations 5444
35M85 Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type [See also 35R35, 49J40] 3
35M86 Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type [See also 35R35, 49J40] 34
35M87 Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type [See also 35R35, 49J40] 16
35Nxx Overdetermined problems for partial differential equations and systems of partial differential equations {For global analysis, see 58Hxx, 58J10, 58J15} 2087
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs [See also 32W05, 32W10, 58J10] 771
35Pxx Spectral theory and eigenvalue problems for partial differential equations {For operator theory, see 47Axx, 47Bxx, 47F05} 24445
35Qxx Partial differential equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] 142192
35Q20 Boltzmann equations {For fluid mechanics, see 76P05; for statistical mechanics, see 82B40, 82C40, 82D05} 2041
35Q41 Time-dependent Schrödinger equations and Dirac equations {For quantum theory, see 81Q05; for relativity and gravitational theory, see 83A05, 83C10} 3325
35Q49 Transport equations {For calculus of variations and optimal control, see 49Q22; for fluid mechanics, see 76F25; for statistical mechanics, see 82C70, 82D75; for operations research, see 90B06; for mathematical programming, see 90C08} 454
35Q53 KdV equations (Korteweg-de Vries equations) {For dynamical systems and ergodic theory, see 37K10} 19704
35Q55 NLS equations (nonlinear Schrödinger equations) {For dynamical systems and ergodic theory, see 37K10} 17053
35Q61 Maxwell equations {For optics and electromagnetic theory, see 78A25; for relativity and gravitational theory, see 83C22} 1845
35Q76 Einstein equations {For several complex variables and analytic spaces, see 32Q40; for differential geometry, see 53C07; for relativity and gravitational theory, see 83C05, 83C25, 83D05} 339
35Q84 Fokker-Planck equations {For fluid mechanics, see 76X05, 76W05; for statistical mechanics, see 82C31} 1806
35Q89 PDEs in connection with mean field game theory {For calculus of variations and optimal control, see 49N80; for game theory, see 91A16} 137
35Rxx Miscellaneous topics in partial differential equations {For equations on manifolds, see 32Wxx, 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see 60H15} 63913
35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) [See also 46Gxx, 58D25] 688
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx] 1614
35Sxx Pseudodifferential operators and other generalizations of partial differential operators {For operator theory, see 47G30, 58J40} 7538
35S05 Pseudodifferential operators as generalizations of partial differential operators [See also 32W25, 47G30, 47L80, 58J40] 4264
35S35 Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15] 107
35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs 156