On the regularity of solutions to integral equations with nonsmooth kernels on a union of open intervals

The behaviour of a solution to a Fredholm integral equation of the second kind on a union of open intervals is examined. The kernel of the corresponding integral operator may have diagonal singularities, information about them is given through certain estimates. The weighted spaces of smooth functio...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 229; no. 2; pp. 440 - 451
Main Authors Pedas, Arvet, Vainikko, Gennadi
Format Journal Article Conference Proceeding
LanguageEnglish
Published Kidlington Elsevier B.V 15.07.2009
Elsevier
Subjects
Boundary singularities
Compact operators
Exact sciences and technology
Fredholm integral equation
Integral equations
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Operator theory
Sciences and techniques of general use
Smoothness of the solution
Weakly singular kernel
45B05
Smoothness of the solution
Fredholm integral equation
45M05
Weakly singular kernel
Boundary singularities
Compact operators
45D05
Integral operator
Fredholm equation
Compact operator
Numerical analysis
Applied mathematics
Weight function
Solution regularity
Smooth function
Integral equation
Singular kernel
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Summary:The behaviour of a solution to a Fredholm integral equation of the second kind on a union of open intervals is examined. The kernel of the corresponding integral operator may have diagonal singularities, information about them is given through certain estimates. The weighted spaces of smooth functions with boundary singularities containing the solution of the integral equation are described.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.04.009