Chikouche, Wided2024-07-122024-07-122019Chikouche, W. (2019). The transmission problem for the laplace operator on a domain with a cuspidal point. International Conference of Mathematical Sciences (ICMS 2019). s. 61.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2905We shall study the transmission problem for the Laplace operator subject to Dirichlet boundary conditions in a plane domain ? with an external cusp, ? being divided into two subdomains ?1 and ?2 separated by a straight interface. We look for a solution in the framework of L p -Sobolev spaces, 1 < p < +?. We prove that u ? H1 0 (?) solution of ?div(p?u) = f with f in L p (?) and p = pi on ?i , i = 1, 2, (p1, p2 are two positive real numbers, supposed to be different), is picewise in W2,p .enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessTransmission problemRegularityCuspidal domainsArticle6161