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§1 INTRODUCTION The work on"Lie group and KDV equations" has been done in[1]. From the structure equations of certain Lie Group, a class of evolution equations of Sine-Gorden type may be achieved. In this paper from a new viewpoint introduced in [2], we will derive a class of evolution equations of Sine-Gorden type. Furthermore we have given geometric interoretations for our evolution equations of Sine-Gorden type. The evolution equations of Sine-Gorden type which have been got in [3] are a special class of our paper. 相似文献
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1.IntroductionCanyouheartheshapeofadrum?ProfessorProtteraskedinhisrevisitedpaperrll'Usually,thiskindofproblemscanmathematicallybesolvedbyestimatingtheboundsoftheeigenvaluestopolyharmonicoperators.IfonestrikessimultaneouslyNdrumsmadebythesamematerialandpossessingthesamesize,weshouldaskthatcanyouheartheshapeofthedrums?Toanswerthisquestion,onemightconsideraneigenvalueproblemforacertainsystemasfollows:wherefiisaboundedsmoothdomaininRe(m22),u=(al)ro,'',urn)istheoutwardunitnormaltotheboundaryoffi… 相似文献
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设是一个有界区域,考虑问题: D_i(g(|Du|~2)|Du|~(p-2)D_iu)=0,x∈Ω其中g(0)=0;当t>0时,g(t)>0.加上g(t)必须满足的条件.利用这些条件,我们获得上述退化椭圆型方程的广义解的局部正则性。 在文中,我们运用了逼近法和证明主要引理的一些技巧。 最后,我们给出两个具体例子。 相似文献
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§1 INTRODUCTION The work on"Lie group and KDV equations" has been done in [1]. From the structure equations of certain Lie Group, a class of evolution equations of Sine-Gorden type may be achieved. In this paper from a new viewpoint introduced in [2], we will derivea class 相似文献
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本文推导斯图姆—刘维尔问题的特征值的上界估计,其估计系数与区间的几何衡量无关,其结果在力学等学科中有着广泛的应用。 相似文献
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ESTIMATESOFEIGENVALUESFORUNIFORMLYELLIPTICOPERATOROFSECONDORDERQIANCHUNLIN(钱椿林)CHENZUCHI(陈祖墀)(DepartmentofMathetnatics,Univer... 相似文献
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