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Balayage

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296: 249: 113: 337: 361: 171: 330: 278: 273: 268: 323: 356: 303: 56: 131: 75: 89: 45: 41: 20: 142: 27: 36: 307: 19:
This article is about the method in mathematics. For the hair painting technique, see
350: 295: 115:. The procedure is called balayage since the mass is "swept out" from 48:
in a domain from its values on the boundary of the domain.
244:{\displaystyle f(x)=\int _{\partial D}f(y)\,d\nu _{x}(y).} 16:
Method for reconstructing a harmonic function in a domain
311: 174: 92: 243: 107: 331: 40:"scanning, sweeping") is a method devised by 8: 338: 324: 223: 215: 194: 173: 94: 93: 91: 157:. Then the value of a harmonic function 259: 21:Hair highlighting § Hair painting 7: 292: 290: 195: 14: 294: 235: 229: 212: 206: 184: 178: 99: 1: 30:, a mathematical discipline, 310:. You can help Knowledge by 362:Mathematical analysis stubs 274:Encyclopedia of Mathematics 267:Solomentsev, E.D. (2001) , 378: 289: 108:{\displaystyle {\bar {D}}} 18: 306:–related article is a 245: 109: 44:for reconstructing an 304:mathematical analysis 246: 110: 51:In modern terms, the 172: 90: 76:Newtonian potentials 119:onto the boundary. 62:on a closed domain 241: 130:, the balayage of 105: 319: 318: 269:"Balayage method" 153:corresponding to 102: 86:coincide outside 53:balayage operator 46:harmonic function 369: 357:Potential theory 340: 333: 326: 298: 291: 282: 281: 264: 250: 248: 247: 242: 228: 227: 202: 201: 143:harmonic measure 114: 112: 111: 106: 104: 103: 95: 70:on the boundary 28:potential theory 377: 376: 372: 371: 370: 368: 367: 366: 347: 346: 345: 344: 287: 285: 266: 265: 261: 257: 219: 190: 170: 169: 152: 139: 88: 87: 24: 17: 12: 11: 5: 375: 373: 365: 364: 359: 349: 348: 343: 342: 335: 328: 320: 317: 316: 299: 284: 283: 258: 256: 253: 252: 251: 240: 237: 234: 231: 226: 222: 218: 214: 211: 208: 205: 200: 197: 193: 189: 186: 183: 180: 177: 148: 135: 101: 98: 74:, so that the 42:Henri PoincarĂ© 34:(from French: 15: 13: 10: 9: 6: 4: 3: 2: 374: 363: 360: 358: 355: 354: 352: 341: 336: 334: 329: 327: 322: 321: 315: 313: 309: 305: 300: 297: 293: 288: 280: 276: 275: 270: 263: 260: 254: 238: 232: 224: 220: 216: 209: 203: 198: 191: 187: 181: 175: 168: 167: 166: 164: 160: 156: 151: 147: 144: 140: 138: 134: 129: 125: 120: 118: 96: 85: 81: 77: 73: 69: 66:to a measure 65: 61: 58: 54: 49: 47: 43: 39: 38: 33: 29: 22: 312:expanding it 301: 286: 272: 262: 165:is equal to 162: 158: 154: 149: 145: 136: 132: 127: 123: 121: 116: 83: 79: 71: 67: 63: 59: 52: 50: 35: 31: 25: 141:yields the 351:Categories 255:References 279:EMS Press 221:ν 196:∂ 192:∫ 100:¯ 72:∂ D 37:balayage 32:balayage 57:measure 55:maps a 146:ν 133:δ 84:ν 80:μ 68:ν 60:μ 302:This 308:stub 122:For 82:and 161:at 126:in 78:of 26:In 353:: 277:, 271:, 339:e 332:t 325:v 314:. 239:. 236:) 233:y 230:( 225:x 217:d 213:) 210:y 207:( 204:f 199:D 188:= 185:) 182:x 179:( 176:f 163:x 159:f 155:x 150:x 137:x 128:D 124:x 117:D 97:D 64:D 23:.

Index

Hair highlighting § Hair painting
potential theory
balayage
Henri Poincaré
harmonic function
measure
Newtonian potentials
δx
harmonic measure
"Balayage method"
Encyclopedia of Mathematics
EMS Press
Stub icon
mathematical analysis
stub
expanding it
v
t
e
Categories
Potential theory
Mathematical analysis stubs

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