{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:36:11Z","timestamp":1746804971676,"version":"3.40.5"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We study the Dirichlet problem for the equation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0394<\/mml:mi><mml:mi>u<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:msup><mml:mi>k<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mi>u<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:math>in the exterior of nonclosed Lipschitz surfaces in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mi>R<\/mml:mi><mml:mn>3<\/mml:mn><\/mml:msup><\/mml:mrow><\/mml:math>. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.<\/jats:p>","DOI":"10.1155\/2013\/302628","type":"journal-article","created":{"date-parts":[[2013,2,13]],"date-time":"2013-02-13T16:01:40Z","timestamp":1360771300000},"page":"1-4","source":"Crossref","is-referenced-by-count":0,"title":["The Dirichlet Problem for the Equation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0394<\/mml:mi><mml:mi>u<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:msup><mml:mi>k<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><mml:mi>u<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:math>in the Exterior of Nonclosed Lipschitz Surfaces"],"prefix":"10.1155","volume":"2013","author":[{"given":"P. A.","family":"Krutitskii","sequence":"first","affiliation":[{"name":"KIAM, Miusskaya Sq. 4, Moscow 125047, Russia"}]}],"member":"311","reference":[{"year":"2000","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(84)90066-1"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1981-14884-9"},{"year":"1985","key":"4"},{"issue":"1","key":"5","doi-asserted-by":"crossref","first-page":"13","DOI":"10.4064\/sm-66-1-13-24","volume":"66","year":"1979","journal-title":"Studia Mathematica"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-009-9075-z"},{"year":"2004","key":"7"},{"key":"8","first-page":"798","volume":"4","year":"1960","journal-title":"Soviet Physics Doklady"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00969506"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/269607"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500020952"},{"issue":"2","key":"12","doi-asserted-by":"crossref","first-page":"361","DOI":"10.4171\/ZAA\/827","volume":"17","year":"1998","journal-title":"Zeitschrift f\u00fcr Analysis und ihre Anwendungen"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19970771202"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/340310"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/302628.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/302628.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/302628.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T14:16:49Z","timestamp":1562681809000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2013\/302628\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":14,"alternative-id":["302628","302628"],"URL":"https:\/\/doi.org\/10.1155\/2013\/302628","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2013]]}}}