INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION

数学物理学报(英文版) ›› 1986, Vol. 6 ›› Issue (4): 361-365.

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INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION

M. I. Hassan

Dept. of Math., Faculty of Science, King Abdulaziz Univ., Jeddah, POB 9028, Saudi Arabia

收稿日期:1983-10-31 出版日期:1986-12-25 发布日期:1986-12-25

INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION

M. I. Hassan

Dept. of Math., Faculty of Science, King Abdulaziz Univ., Jeddah, POB 9028, Saudi Arabia

Received:1983-10-31 Online:1986-12-25 Published:1986-12-25

摘要/Abstract

摘要： The main result concerning the question of whether the classical solution u(x) of Dirichlet's problem for an elliptic equation Lu=f is in the Sobolev space W¹ is that u∈W¹ provided the coefficients of L areessentially bounded and f∈L². Here, the author proves a result showing that u may be in W¹ even when f is not in the class L².

M. I. Hassan. INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION[J]. 数学物理学报(英文版), 1986, 6(4): 361-365.

M. I. Hassan. INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION[J]. Acta mathematica scientia,Series B, 1986, 6(4): 361-365.

INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION

INTEGRABILITY OF DERIVATIVES OF CLASSICAL SOLUTIONS OF DIRICHLET'S PROBLEM FOR AN ELLIPTIC EQUATION

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