Index
Adjoint operator *A,4
Balayage // = B(ji; dS) of a measure fx ,
30
Capacity, 23
Center of gravity, 28
Characteristic (lower) conoid cono(x, t),
163
Coefficients (identification)
problem, xi
Complex potential Uz(z; //), 46
Conditionally (by Tikhonov) correct
problem, xii
Cone con(x; e), 24
(lower) cone conc(x, t), 162
Cone condition, 24
Conormal v , 4
Convexity in x{ , 36
Density problem, 34
Domain problem, 34
Ellipticity, 7
Energy inequalities, 67
Extremum principles, 11
Fundamental solution, 14
Giraud's (extremum) principle, 11
Green's formula, 4
Green's function, 14
Hodograph type map, 91
Holder norms | \k , 1
[ ] k ' n \
spaces C , C0 , 2
Ck,k/2 , 137
Hopfs (extremum) principle, 11
Indicator function /(5) , 1
Inverse problem of potential theory, 33
Inverse diffraction problem, 35
Inverse magnetic exploration problem, 35
Jump formulae, 19
Kelvin transform, 17
KirchhofFs formula, 163
Lebesgue measure meas^ , dx , 1
Lipschitz functions, sets, 2
Measure, 15
Monotonicity principle, 139
Obstacle problem, 108
Operator L , 21
Operator L^, 30
Orthogonality method, 37
Parabolic boundary value problem, 137
Parabolic equation, 7
Parabolic, thermal potentials U(x, t; f),
140
Parametrix # (0 ) , 14
Potentials of a measure £/(•; ju), 15
of double layer U2 , 18
of simple layer Ul = U(-; gdT), 16
of volume £/(•; f), t/(-;/(Q)), 16
m-principal part Am of ^ , 5
Regular points of the boundary, 23
Regularization, 40
Regularized equation, 41
Riesz potentials, 38, 79
Sobolev norms || \\k^p, || \\{k) , 3
spaces HktP, Hk,p, H{k) =Hk'2 , 3
("minimal") Speed of propagation, 173
Stability (instability) points, 24
Stabilizing functional, 42
Stable Dirichlet problem, 25
Star-shaped set, 36
Support of a function u, supp u , 2
Symbol A(x;Q of A , 5
Wave operator Dc , , 50, 161
Well-posed (by Hadamard) problem, xii
Wiener's (generalized) solution u , 22
x-boundary dxQ, 140
193
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