一种低正则系数对应时谐麦克斯韦方程解的唯一性
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摘要
通过反证法将齐次线性椭圆方程解的唯一性延伸至具有小能量非齐次项的椭圆方程解的唯一性,并且将这种方法应用于麦克斯韦方程,从而获得了当系数正则性足够接近W~(1,∞)时解的唯一性.
This paper mainly develops a reduction method,and by applying the method,the uniqueness of the solution of linear homogeneous elliptic equations is extended to a linear inhomogeneous elliptic equations with a small inhomogeneous term.The argument is applied to the uniqueness for solutions of time harmonic Maxwell's equations with coefficients sufficiently close to W~(1,∞).
This paper mainly develops a reduction method,and by applying the method,the uniqueness of the solution of linear homogeneous elliptic equations is extended to a linear inhomogeneous elliptic equations with a small inhomogeneous term.The argument is applied to the uniqueness for solutions of time harmonic Maxwell's equations with coefficients sufficiently close to W~(1,∞).
引文
[1] RONSZAJN N,LAWRENCE K U.A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order[J].Defense Technical Information Center,1957,36:235.
[2] CAKONI F,COLTON D.A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media[J].Proceedings of the Edinburgh Mathematical Society,2003,46(2):293.
[3] NGUYEN T,WANG J N.Quantitative uniqueness estimate for the Maxwell system with Lipschitz anisotropic media[J].Proc Amer Math Soc,2011,140:595.
[4] OKAJI T.Strong unique continuation property for time harmonic Maxwell equations[J].J Math Soc Jpn,2002,54:89.
[5] BALL J M,APDEBOSCQ Y,BASANG Tsering-xiao.On uniqueness for the time harmonic anisotropic Maxwell equations with piecewise regular coefficients[J].Mathematical Models and Methods in Applied Science,2012,22(11):1.
[6] 小巴桑次仁.各向同性麦克斯韦方程在系数为弱正则时解的唯一性证明[J].西南大学学报(自然科学版), 2013,38(10):1.
[7] 小巴桑次仁.在系数矩阵满则特殊条件下麦克斯韦方程系统解的唯一性[J].西藏大学学报(自然科学版),2012,27(1):111.
[8] 小巴桑次仁.Rellich引理的新证明[J].数学物理学报,2014,34(6):1435.
[2] CAKONI F,COLTON D.A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media[J].Proceedings of the Edinburgh Mathematical Society,2003,46(2):293.
[3] NGUYEN T,WANG J N.Quantitative uniqueness estimate for the Maxwell system with Lipschitz anisotropic media[J].Proc Amer Math Soc,2011,140:595.
[4] OKAJI T.Strong unique continuation property for time harmonic Maxwell equations[J].J Math Soc Jpn,2002,54:89.
[5] BALL J M,APDEBOSCQ Y,BASANG Tsering-xiao.On uniqueness for the time harmonic anisotropic Maxwell equations with piecewise regular coefficients[J].Mathematical Models and Methods in Applied Science,2012,22(11):1.
[6] 小巴桑次仁.各向同性麦克斯韦方程在系数为弱正则时解的唯一性证明[J].西南大学学报(自然科学版), 2013,38(10):1.
[7] 小巴桑次仁.在系数矩阵满则特殊条件下麦克斯韦方程系统解的唯一性[J].西藏大学学报(自然科学版),2012,27(1):111.
[8] 小巴桑次仁.Rellich引理的新证明[J].数学物理学报,2014,34(6):1435.