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On Singular Sets of Local Solutions to p-Laplace Equations 被引量：1

On Singular Sets of Local Solutions to p-Laplace Equations
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摘要 The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the
作者 Hongwei LOU
机构地区 Key Laboratory of Mathematics for Nonlinear Sciences
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2008年第5期521-530,共10页 数学年刊（B辑英文版）
基金 the National Natural Science Foundation of China (No. 10671040) the Foundationfor the Author of National Excellent Doctoral Dissertation of China (No. 200522) the Program forNew Century Excellent Talents in University of China (No. 06-0359)
关键词 Singular set p-Laplace equation Optimal control EXISTENCE 单数集 局部解 P拉普拉斯方程式 最优控制理论
分类号 O175.27 [理学—基础数学] O232 [理学—运筹学与控制论]
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参考文献10

  • 1Casas, E. and Fernandez, L. A., Distributed control of systems governed by a general class of quasilinear elliptic equations, Jour. Diff. Eqs., 104, 1993, 20-47.
  • 2DiBenedetto, E., C^1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis, T. M. A., 7, 1983, 827-850.
  • 3Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer-Verlag, Berlin, 1983.
  • 4Kinderlehrer, D. and Stampacchia, G., An Introduction to Variational Inequalities, Academic Press, New York, 1981.
  • 5Lou, H. W., Existence of optimal controls for semilinear elliptic equations without Cesari type conditions, ANZIAM J., 45, 2003, 115-131.
  • 6Lou, H. W., Existence of optimal controls for semilinear parabolic equations without Cesari type conditions, Appl. Math. Optim., 47, 2003, 121-142.
  • 7Morrey, C. B. Jr., Existence and differentiability theorems for variational problems for multiple integrals, Partial Differential Equations and Continuum Mechanics, Univ. of Wisconsin Press, Madison, 1961, 241- 270.
  • 8Moser, J., On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math., 14, 1961, 577-591.
  • 9Tolksdorf, P., Regularity for a more general case of quasilinear elliptic equations, J. Diff. Eqs., 51, 1984, 126-150.
  • 10Troianiello, G. M., Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987.

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Chinese Annals of Mathematics,Series B
2008年 第5期

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