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Title: Generalized and Classical Maximum Principle For Class of Second Order Elliptic Systems
Authors: Mohammad Mujalli Al-mahameed
Keywords: Generalized and Classical Maximum Principle For Class of Second Order Elliptic Systems
Classical Maximum Principle
Second Order Elliptic Systems
Issue Date: 20-Oct-2003
Abstract: الملخص في هذا البحث أوجدنا أحد مبادئ القيم العظمى المعممة لأنظمة من المعادلات التفاضلية الجزئية الناقصة المتجانسة من المرتبة الثانية ذات الارتباط الضعيف. وأوجدنا كذلك شرطاً ضرورياً لمبدأ القيمة العظمى التقليدي. هذه النتائج هي تطوير لبعض النتائج حول مبادئ القيم العظمى التي وردت في المراجع المذكورة في البحث ولكن تحت شروط مختلفة. Abstract In this paper we find a generalized maximum principle for weakly coupled second order homogeneous elliptic systems Lu Au = 0 in ? ? Rn Where L [u(x)]= aij(x) ai (x) , aij = aji is a second order real elliptic operator, u=(u1, u2, ? ?, un)T, and A is an n ? ? n matrix with entries which are all complex valued functions. We also find a sufficient condition for the classical maximum principle. These results extend the result of Winter and Wong [12] for A being negative semidefinite to a more general form of A. Generalized maximum principles for weakly coupled second order elliptic systems have also been obtained by Dow [2], Hile and Protter [6], and Wasowski [11] under different conditions on the coefficients.
URI: http://hdl.handle.net/123456789/555
Appears in Collections:المجلد 12 العدد 2

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