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Monge equation

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674: 22: 560: 301: 342: 156: 715: 128: 734: 555:{\displaystyle \sum _{i_{0}+\cdots +i_{n}=k}P_{i_{0}\dots i_{n}}(x_{0},x_{1},\dots ,x_{k})\,dx_{0}^{i_{0}}\,dx_{1}^{i_{1}}\cdots dx_{n}^{i_{n}}=0} 32: 739: 296:{\displaystyle F\left(u,x_{1},x_{2},\dots ,x_{n},{\frac {\partial u}{\partial x_{1}}},\dots ,{\frac {\partial u}{\partial x_{n}}}\right)=0} 655: 708: 116: 90: 47: 62: 597: 642: 69: 701: 647: 566: 76: 58: 681: 617: 651: 83: 685: 728: 124: 112: 21: 315: 307: 673: 593:) is the zero locus of the equation in the tangent space at the point. 640:
Rozov, N. Kh. (1990). "Monge equation". In Hazewinkel, Michiel (ed.).
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The Monge equation is unrelated to the (second-order)
345: 159: 554: 295: 709: 8: 48:introducing citations to additional sources 716: 702: 538: 533: 528: 510: 505: 500: 492: 484: 479: 474: 466: 457: 438: 425: 410: 397: 392: 374: 355: 350: 344: 273: 255: 237: 219: 210: 191: 178: 158: 129:first-order partial differential equation 38:Relevant discussion may be found on the 609: 565:and expresses a relation between the 7: 670: 668: 577:. The Monge cone at a given point ( 266: 258: 230: 222: 14: 672: 31:relies largely or entirely on a 20: 735:Partial differential equations 463: 418: 310:in the partial derivatives of 117:partial differential equations 1: 332:, a Monge equation of degree 135:in the independent variables 688:. You can help Knowledge by 314:. Any Monge equation has a 740:Mathematical analysis stubs 643:Encyclopedia of Mathematics 756: 667: 648:Kluwer Academic Publishers 131:for an unknown function 336:is written in the form 684:–related article is a 556: 297: 682:mathematical analysis 598:Monge–Ampère equation 557: 321:Classically, putting 298: 343: 157: 44:improve this article 545: 517: 491: 552: 524: 496: 470: 387: 293: 697: 696: 584:, ...,  346: 280: 244: 109: 108: 94: 747: 718: 711: 704: 676: 669: 661: 632: 631: 629: 628: 614: 561: 559: 558: 553: 544: 543: 542: 532: 516: 515: 514: 504: 490: 489: 488: 478: 462: 461: 443: 442: 430: 429: 417: 416: 415: 414: 402: 401: 386: 379: 378: 360: 359: 302: 300: 299: 294: 286: 282: 281: 279: 278: 277: 264: 256: 245: 243: 242: 241: 228: 220: 215: 214: 196: 195: 183: 182: 104: 101: 95: 93: 59:"Monge equation" 52: 24: 16: 755: 754: 750: 749: 748: 746: 745: 744: 725: 724: 723: 722: 665: 658: 646:. Vol. 6. 639: 636: 635: 626: 624: 616: 615: 611: 606: 592: 583: 576: 534: 506: 480: 453: 434: 421: 406: 393: 388: 370: 351: 341: 340: 331: 269: 265: 257: 233: 229: 221: 206: 187: 174: 167: 163: 155: 154: 150: 141: 105: 99: 96: 53: 51: 37: 25: 12: 11: 5: 753: 751: 743: 742: 737: 727: 726: 721: 720: 713: 706: 698: 695: 694: 677: 663: 662: 656: 634: 633: 618:"Monge method" 608: 607: 605: 602: 588: 581: 572: 563: 562: 551: 548: 541: 537: 531: 527: 523: 520: 513: 509: 503: 499: 495: 487: 483: 477: 473: 469: 465: 460: 456: 452: 449: 446: 441: 437: 433: 428: 424: 420: 413: 409: 405: 400: 396: 391: 385: 382: 377: 373: 369: 366: 363: 358: 354: 349: 329: 304: 303: 292: 289: 285: 276: 272: 268: 263: 260: 254: 251: 248: 240: 236: 232: 227: 224: 218: 213: 209: 205: 202: 199: 194: 190: 186: 181: 177: 173: 170: 166: 162: 146: 139: 123:, named after 121:Monge equation 107: 106: 42:. Please help 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 752: 741: 738: 736: 733: 732: 730: 719: 714: 712: 707: 705: 700: 699: 693: 691: 687: 683: 678: 675: 671: 666: 659: 657:1-55608-005-0 653: 649: 645: 644: 638: 637: 623: 622:evlm.stuba.sk 619: 613: 610: 603: 601: 599: 594: 591: 587: 580: 575: 571: 568: 567:differentials 549: 546: 539: 535: 529: 525: 521: 518: 511: 507: 501: 497: 493: 485: 481: 475: 471: 467: 458: 454: 450: 447: 444: 439: 435: 431: 426: 422: 411: 407: 403: 398: 394: 389: 383: 380: 375: 371: 367: 364: 361: 356: 352: 347: 339: 338: 337: 335: 328: 325: =  324: 319: 317: 313: 309: 290: 287: 283: 274: 270: 261: 252: 249: 246: 238: 234: 225: 216: 211: 207: 203: 200: 197: 192: 188: 184: 179: 175: 171: 168: 164: 160: 153: 152: 151: 149: 145: 138: 134: 130: 126: 125:Gaspard Monge 122: 118: 114: 103: 92: 89: 85: 82: 78: 75: 71: 68: 64: 61: â€“  60: 56: 55:Find sources: 49: 45: 41: 35: 34: 33:single source 29:This article 27: 23: 18: 17: 690:expanding it 679: 664: 641: 625:. Retrieved 621: 612: 595: 589: 585: 578: 573: 569: 564: 333: 326: 322: 320: 311: 305: 147: 143: 136: 132: 120: 113:mathematical 110: 100:January 2022 97: 87: 80: 73: 66: 54: 30: 729:Categories 627:2022-10-16 604:References 316:Monge cone 308:polynomial 306:that is a 115:theory of 70:newspapers 519:⋯ 448:… 404:… 365:⋯ 348:∑ 267:∂ 259:∂ 250:… 231:∂ 223:∂ 201:… 40:talk page 127:, is a 111:In the 84:scholar 654:  86:  79:  72:  65:  57:  680:This 142:,..., 91:JSTOR 77:books 686:stub 652:ISBN 119:, a 63:news 46:by 731:: 650:. 620:. 600:. 570:dx 318:. 717:e 710:t 703:v 692:. 660:. 630:. 590:n 586:x 582:0 579:x 574:k 550:0 547:= 540:n 536:i 530:n 526:x 522:d 512:1 508:i 502:1 498:x 494:d 486:0 482:i 476:0 472:x 468:d 464:) 459:k 455:x 451:, 445:, 440:1 436:x 432:, 427:0 423:x 419:( 412:n 408:i 399:0 395:i 390:P 384:k 381:= 376:n 372:i 368:+ 362:+ 357:0 353:i 334:k 330:0 327:x 323:u 312:u 291:0 288:= 284:) 275:n 271:x 262:u 253:, 247:, 239:1 235:x 226:u 217:, 212:n 208:x 204:, 198:, 193:2 189:x 185:, 180:1 176:x 172:, 169:u 165:( 161:F 148:n 144:x 140:1 137:x 133:u 102:) 98:( 88:· 81:· 74:· 67:· 50:. 36:.

Index


single source
talk page
improve this article
introducing citations to additional sources
"Monge equation"
news
newspapers
books
scholar
JSTOR
mathematical
partial differential equations
Gaspard Monge
first-order partial differential equation
polynomial
Monge cone
differentials
Monge–Ampère equation
"Monge method"
Encyclopedia of Mathematics
Kluwer Academic Publishers
ISBN
1-55608-005-0
Stub icon
mathematical analysis
stub
expanding it
v
t

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