Vladimir Vasilyev, Chair of Pure Mathematics, Lipetsk State Technical University, Moskovskaya 30, Lipetsk 398600, Russia, e-mail: vladimir.b.vasilyev@gmail.com
Abstract: We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems, related to Dirichlet and Neumann boundary conditions, are considered. A certain integral representation for this case is given.
Keywords: wave factorization; pseudodifferential equation; boundary value problem; integral equation
Classification (MSC 2010): 35J40, 42A38
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