Solvability of the Dirichlet Problem in W^(2,p )for a Class of Elliptic Equations with Singular Data
Solvability of the Dirichlet Problem in W^(2,p )for a Class of Elliptic Equations with Singular Data
摘要
We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.
We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.
参考文献30
-
1Adams, R. A.: Sobolev Spaces, Academic Press, New York, 1975.
-
2Benci, V., Fortunato, D.: Weighted Sobolev spaces and the nonlinear Dirichlet problem in unbounded domains. Ann. Mat. Pura Appl., 121, 319-336 (1979).
-
3Boccia, S., Monsurro, S., Transirico, M.: Elliptic equations in weighted Sobolev spaces on unbounded domains. Int. J. Math. Math. Sei., 2008, Art. ID 582435, 12 pp (2008).
-
4Boccia, S., Monsurro, S., Transirico, M.: Solvability of the Diriehlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains. Bound. Value Probl., 2008, Art. ID 901503, 13 pp (2008).
-
5Canale, A., Caso, L., Di Gironimo, P.: Weighted norm inequalities on irregular domains. Rend. Accad. Naz. Sci. XL Mere. Mat., 16, 193-209 (1992).
-
6Canale, A., Caso, L., Transirieo, M.: Second order elliptic equations with discontinuous coefficients in irregular domains. Rend. Accad. Naz. Sci. XL Mere. Mat. Appl., 24, 63-79 (2000).
-
7Caso, L.: Regularity results for singular elliptic problems. J. Funct. Spaces Appl., 4, 243 259 (2006).
-
8Caso, L.: Properties of weak solutions of an elliptic problem in weighted spaces. Int. J. Pure Appl. Math., 62, 151-166 (2010).
-
9Caso, L., Cavaliere, P., Transirieo, M.: A priori bounds for elliptic equations. Ricerche Mat., 51, 381-396 (2002).
-
10Caso, L., Cavaliere, P., Transirico, M.: Existence results for elliptic equations. J. Math. Anal. Appl., 274, 554 563 (2002).
-
1尚世亮,庞耀辉.对两道不等式问题证明的研究[J].中学数学研究,2005(1):19-20.
-
2王建平,王洪林,张敏.积分上限函数在中值问题证明中的应用[J].河北工程技术高等专科学校学报,2013(2):51-54.
-
3刘冬兵,马亮亮,陈龙.基于插值法的中值问题证明[J].温州大学学报(自然科学版),2012,33(5):28-32.
-
4柳合龙,宋新宇.一类半线性椭圆型方程正解的唯一性[J].信阳师范学院学报(自然科学版),1998,11(2):116-119.
-
5汪俭彬,黄瑞芳.泰勒公式在解决典型问题方面的应用研究[J].焦作师范高等专科学校学报,2011,27(2):76-77. 被引量:2
-
6陈恕行,王亚光.THE CAUCHY PROBLEM FOR GAS DYNAMIC SYSTEMS IN MULTI-DIMENSIONAL SPACE WITH WEAKLY SINGULAR DATA[J].Chinese Annals of Mathematics,Series B,1992,13(3):298-314.
-
7朱其超.用数学归纳法证题需当心这几点[J].数学教学通讯(教师阅读),2010(3):59-60.
-
8徐彦辉.一道竞赛题的解答及推广[J].数学通报,2010,49(8):63-64. 被引量:1
-
9欧阳尚昭.构造数学问题证明组合恒等式[J].数学大世界(教学导向),2003(7):15-16.
-
10赵普军.中值问题的证明技巧[J].科技风,2008(4):98-99.