Curvilinear integrals of discontinuous functions over nonrectifiable paths and Riemann boundary‐value problem
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DOI: 10.1002/mma.5474
Abstract: We study a generalization of the concept of curvilinear integral for the case where path of integration is nonrectifiable, and integrand has discontinuities. Then we apply that integrals for solving of the Riemann boundary‐value problem… read more here.
Keywords: boundary value; value problem; curvilinear integrals; riemann boundary ... See more keywords
On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
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DOI: 10.1007/s13324-018-0210-3
Abstract: The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro… read more here.
Keywords: dimensional helmholtz; riemann boundary; helmholtz equation; boundary value ... See more keywords
Riemann boundary-value problem for doubly-periodic bianalytic functions
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DOI: 10.1186/s13661-018-1005-z
Abstract: In this paper, we study Riemann boundary-value problem for doubly-periodic bianalytic functions. By the decomposition of doubly-periodic polyanalytic functions, the problem is transformed into two equivalent and independent Riemann boundary-value problems of doubly-periodic analytic functions,… read more here.
Keywords: riemann boundary; doubly periodic; boundary value; periodic bianalytic ... See more keywords
On Riemann Boundary-Value Problem for Regular Functions in Clifford Algebras
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DOI: 10.3103/s1066369x18010061
Abstract: We pose and investigate the Riemann boundary-value problem for regular and strongly regular functions in Clifford algebras. The posed problem is reduced to the matrix problem for analytical functions in one and two complex variables… read more here.
Keywords: riemann boundary; value problem; boundary value; problem regular ... See more keywords