Geodesic
On the application of the regularization method to the construction of a classical solution of Poisson's equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 196-211

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Necessary and sufficient conditions are found for the existence of a classical solution of Poisson's equation $\Delta u=f$ with continuous function $f$ in a bounded planar domain. By virtue of the known smoothness properties of a generalized harmonic function, these conditions also ensure that all generalized solutions of Poisson's equation are classical in this domain. Particular classes of functions $f$ satisfying the conditions of existence of a classical solution are described.
Mots-clés : Poisson's equation
Keywords: classical and generalized solutions, harmonic function, continuous function, strongly continuous function, uniformly strongly continuous function. 
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     title = {On the application of the regularization method to the construction of a classical solution of {Poisson's} equation},
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È. M. Muhamadiev; G. E. Grishanina; A. A. Grishanin. On the application of the regularization method to the construction of a classical solution of Poisson's equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 196-211. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a17/