INDEX 751
Laplace’s equation, 25, 26, 85
measurable
function, 734
strongly, 736
weakly, 736
sets, 733
method of descent, 74, 78, 694
minimal surface equation, 5, 210, 459
minimax methods, 370, 507–513
minimizer, 457, 462
existence of, 467–473, 477, 481
local, 482–484
regularity, 484–489
uniqueness of, 473
mixed boundary conditions, 368
mollifier, 266, 716
momentum, generalized, 118
Monge–Amp` ere equation, 5
Monotone Convergence Theorem, 471,
735
monotonicity, 11, 529–535, 563
strict, 534
monotonicity formula
p-Laplacian, 517
Almgren’s, 527
Laplace’s equation, 527
Morawetz identity, 520, 683
Morse Lemma, 224
Mountain Pass Theorem, 507, 512
moving plane method, 560–561
multiindices, 13, 703
Multinomial Theorem, 13, 239
multipliers, 513–521
multivalued equation, 525, 567, 568
N-wave, 157
Navier–Stokes equations, 6
Neumann boundary conditions, 368
Newton’s law, 66, 118, 613
Noether’s Theorem, 513–522
noncharacteristic
boundary data, 104, 105, 163
surface, 235, 236, 238
nonconvex flux function, 658–659
nondivergence form PDE, 314, 374
nonexistence of solutions, 549–556,
641–643, 688–693, 697
nonhomogeneous problem
heat equation, 49, 51
transport equation, 19
wave equation, 80
nonlinear eigenvalue problem, 491
nonlinear Schr¨odinger (NLS) equation,
697
norm, 257, 722, 723
normal
derivative, 713
to surface, 713
notation
for estimates, 706
for functions, 701–705
for matrices, 699–700
geometric, 700–701
null Lagrangian, 463, 465, 523, 524
O, o notation, 706
obstacle problem, 494
Ohm’s law, 21
Oleinik, O., 166
optimality conditions, 594
orthogonality, 724
p-Laplacian, 5, 516
monotonicity formula, 517
p-system, 612, 651
generalization of, 656
traveling waves for, 646
Palais–Smale condition, 504, 505, 507,
511
parabolic
approximation, 216
boundary, 52
cylinder, 52
parabolicity, 374
partial derivatives, 13, 703
count of, 12
partial differential equation
definition of, 1
partition of unity, 267, 269, 272, 276,
308
pattern formation, 175
penalty method, 576
periodic solution, 230–233, 576
Perron–Frobenius Theorem, 356
phase, 219
plane, 181
velocity, 178, 695
Plancherel’s Theorem, 187
plane wave, 176, 178, 197, 424
Poisson’s
equation, 20, 23, 315, 448
nonlinear, 5, 459
formula
ball, 41, 86, 87
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