{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:16:30Z","timestamp":1753888590360,"version":"3.41.2"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,7,5]],"date-time":"2006-07-05T00:00:00Z","timestamp":1152057600000},"content-version":"vor","delay-in-days":185,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"This paper studies the third problem for the Laplace equation on a\nbounded planar domain with inside cracks. The third condition\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\u2202<\/jats:italic>u<\/jats:italic>\/\u2202<\/jats:italic>n<\/jats:italic> + h<\/jats:italic>u<\/jats:italic> = f<\/jats:italic>\n is given on the boundary of the\ndomain. The skip of the function u<\/jats:italic>+<\/jats:sub> \u2212 u<\/jats:italic>\u2212<\/jats:sub> = g<\/jats:italic>\n and the modified\nskip of the normal derivatives (\u2202<\/jats:italic>u<\/jats:italic>\/\u2202<\/jats:italic>n<\/jats:italic>)\u2009+<\/jats:sub> \u2212 (\u2202<\/jats:italic>u<\/jats:italic>\/\u2202<\/jats:italic>n<\/jats:italic>)\u2009\u2212<\/jats:sub> + h<\/jats:italic>u<\/jats:italic>+<\/jats:sub> = f<\/jats:italic>\n are given on cracks. The\nsolution is looked for in the form of the sum of a modified\nsingle\u2010layer potential and a double\u2010layer potential. The solution\nof the corresponding integral equation is constructed.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/91983","type":"journal-article","created":{"date-parts":[[2006,8,2]],"date-time":"2006-08-02T19:13:45Z","timestamp":1154546025000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The solution of the third problem for the Laplace equation onplanar domains with smooth boundary and inside cracks and modifiedjump conditions on cracks"],"prefix":"10.1155","volume":"2006","author":[{"given":"Dagmar","family":"Medkov\u00e1","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,7,5]]},"reference":[{"key":"e_1_2_1_1_2","unstructured":"Heuser Funktionalanalysis 1975 B. G. Teubner Stuttgart."},{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"KenigC. E. 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