Geodesic
Complex partial differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 54-69

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The Schwarz and iterated Dirichlet boundary-value problems are reported on for the polyanalytic operator in certain plane domains having a harmonic Green function. Hybrid polyharmonic Green functions are reviewed upon which open a variety of boundary-value problems for the polyharmonic operator. This topic is far from being complete. The higher the order of the polyharmonic operator the richer is the theory of related hybrid Green functions: they are constructed by continued convoluting harmonic Green, Neumann, Robin functions also incorporating polyharmonic Green–Almansi functions.
Keywords: polyanalytic operator, Cauchy–Schwarz–Pompeiu representation, Green function, Schwarz boundary-value problem, Dirichlet boundary-value problem, ring domain, Green–Almansi function, polyharmonic hybrid Green function, polyharmonic boundary-value problem, Riquier boundary-value problem.
Mots-clés : admissible domain 
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     title = {Complex partial differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {54--69},
     publisher = {mathdoc},
     volume = {188},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_188_a4/}
}
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Aksoy; H. Begehr; A. Çelebi; B. Shupeyeva. Complex partial differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 54-69. http://geodesic.mathdoc.fr/item/INTO_2020_188_a4/