On the Solvability of a Hypersingular Integral Equation on a Surface with Isothermal Coordinatesстатья
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Дата последнего поиска статьи во внешних источниках: 24 ноября 2021 г.
Аннотация:We study the solvability of one hypersingular integral equation on a smooth surfacewith boundary under the assumption that there exist global isothermal coordinates on thesurface. The integral is understood in the sense of the Hadamard finite value, and the solutionis sought in the class of functions that are H¨older continuous, vanish at the boundary of thesurface, and have surface gradient H¨older continuous in some neighborhood of each point thatdoes not lie on the boundary of the surface. The Fredholm alternative is proved for this equation.It is also shown that the results obtained can be applied to the boundary integral equation arisingin the boundary value problem for the Helmholtz equation in the domain outside this surfacewith the Neumann condition on the surface.