- 期刊
INTEGRABILITY OF DERIVATIONS OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION
並列摘要
The present work is concerned with integrability properties of derivatives of classical solutions of Dirichlet's problem for a linear second-order elliptic equation Lu = f. With the aid of special weighted Hilbert spaces of locally square integrable functions, we determine the nature of singularities that f can have near 1 the boundary, in order that such classical solutions are in the Sobolev space W. By means of an example it is shown that the obtained result is exact.
延伸閱讀
- Hu, Y., & Yang, Z. D. (2013). Analytic Solution of a Class of Fractional Differential Equations. Abstract and Applied Analysis, 2013(), 191-195. https://doi.org/10.1155/2013/109582
- Liu, L. (2013). Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points. Journal of Applied Mathematics, 2013(), 321-329-632. https://doi.org/10.1155/2013/726076
- Chen, Y. J. (2013). On the Existence and Uniqueness of Solutions for Some Elliptic Partial Differential Equations [doctoral dissertation, Tamkang University]. Airiti Library. https://doi.org/10.6846/TKU.2013.00167
- Caso, L., D'Ambrosio, R., & Transirico, M. (2015). W^(-2, p)Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data. Abstract and Applied Analysis, (2015), 1668-1674. https://doi.org/10.1155/2015/635035
- 楊惠文（2009）。The discussion of nonexistence solutions for the elliptic partial differential equation〔碩士論文，大同大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0081-0607200917250401