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Pseudodifferential equations, wave factorization, and related problems
Author(s) -
Vasilyev Vladimir B.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5212
Subject(s) - mathematics , sobolev space , pseudodifferential operators , boundary value problem , wave equation , elliptic curve , mathematical analysis , elliptic operator , factorization , representation (politics) , space (punctuation) , algebra over a field , pure mathematics , algorithm , linguistics , philosophy , politics , political science , law
We consider a model elliptic pseudodifferential equation in a special canonical domains of a multidimensional space. Using a special representation for an elliptic symbol, we give the formula for a general solution of such an equation and choose additional conditions under which this boundary value problem has a unique solution in appropriate Sobolev‐Slobodetskii spaces. Also, we introduce some transmutation operators that help us in constructing the solution.