Index

Admissible function, 231

Balayage measure, 11, 183

Boundary Harnack principle, 99

Conformal cusp, 6, 237

Continuous reflection property, 31

Corner with interior angle ϕ, 3

Cusp, 2, 3

Cusp with a single gauge, 241

Degenerate point, 2

Dirac measure, 11

Domain with quasi-smooth boundary, 17

Double point, 2

First fundamental inequality, 53, 258

Function of bounded variation, 77

Function with a single gauge, 243

Function with gauges, 232

Green function, 12

Harmonic measure, 11

Harnack constant, 52

Harnack principle, 52

Hele-Shaw flow, 1

classical solution, 2

weak solution, 2

Intermediately increasing function, 242

Laminar-flow point, 3

Laminar-flow stationary corner with

interior angle ϕ, 3

Lipschitz constant, 138

Lipschitz continuous function, 138

Local-reflection line, 159

Local-Reflection Theorem, 123

Local-reflexible cusp, 158

Localization Theorem, 22

Lyapunov-Dini corner with a right angle,

51, 76

Lyapunov-Dini cusp, 93

Lyapunov-Dini smooth arc, 51

Martin function, 17

Microlocalization Theorem, 96

Oscillating cusp, 246

Power cusp, 6, 237

Power function, 6, 237

Properly open cusp, 5, 91

Quadrature domain, 9

Quadrilateral in a wide sense, 32

Quasi-laminar-flow point, 3

Radon-Nikod´ ym derivative, 11

Rapidly increasing function, 242

Real-analytic cusp, 5, 237

Reflexible (set), 25

Reflexible cusp, 239

Regular point, 2

Regularity Theorem, 2

Restricted quadrature domain and

measure, 10

Restricted quadrature domain and measure

with weight, 112

Restriction domain, 10

Schwarz function, 6

Second fundamental inequality, 53

Slowly increasing function, 242

Stationary point, 3, 261

Turbulent-flow point, 4, 251

Unbounded variation cusp, 247

269