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