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      退化線性橢圓方程非常弱解的存在唯一性

      2014-11-28 17:56:57晏華輝顧廣澤

      晏華輝+顧廣澤

      摘要:定義了在所謂的具有一片平的邊界的有界光滑區(qū)域內(nèi)退化線性橢圓的非常弱解的概念,然后利用變法方法與退化橢圓方程的極值原理等證明了該問(wèn)題非常弱解的存在唯一性結(jié)果.

      關(guān)鍵詞:存在性; 唯一性; 非常弱解; 退化橢圓方程

      中圖分類號(hào):O175.25 文獻(xiàn)標(biāo)識(shí)碼:A

      他們需要得到上面問(wèn)題非常弱解的存在唯一性結(jié)果.

      [1]QUITTNER P, REICHEL W. Very weak solutions to elliptic equations with nonlinear Neumann boundary conditions [J]. Calc Var Partial Diff Equ,2008,32(4): 429-452.

      [2]BIDAUTVERON M F, PONCE A, VERON L. Boundary singularities of positive solutions of some nonlinear elliptic equations [J]. C R Acad Sci Paris Ser I Math, 2007,344(2): 83-88.

      [3]HU B. Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition [J]. Differential Integral Equations. 1994,7(2): 301-313.

      [4]MCKENNA P J, REICHEL W. A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains [J]. J Funct Anal, 2007,244(1) : 220-246.

      [5]PACARD F. Existence de solutions faibles positive de dans des ouverts bornes de [J]. C R Acad Sci Paris Ser. I Math, 1992,315(7) : 793-798.

      [6]PACARD F. Existence and convergence of positive weak solutions of in a bounded domains of [J]. Calc Var Partial Diff Equ, 1993, 1(3) : 243-265.

      [7]QUITTNER P, SOUPLET PH. A priori estimates and existence for elliptic systems via bootstrap in a weighted Lebesgue spaces [J]. Arch Ration Mech Anal, 2004, 174(1): 49-81.

      [8]CABRE X, SIRE Y. Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates [J]. Ann Inst H Poincar\'{e} Anal NonLin\'{e}aire, 2014,31(1) : 23-53.

      摘要:定義了在所謂的具有一片平的邊界的有界光滑區(qū)域內(nèi)退化線性橢圓的非常弱解的概念,然后利用變法方法與退化橢圓方程的極值原理等證明了該問(wèn)題非常弱解的存在唯一性結(jié)果.

      關(guān)鍵詞:存在性; 唯一性; 非常弱解; 退化橢圓方程

      中圖分類號(hào):O175.25 文獻(xiàn)標(biāo)識(shí)碼:A

      他們需要得到上面問(wèn)題非常弱解的存在唯一性結(jié)果.

      [1]QUITTNER P, REICHEL W. Very weak solutions to elliptic equations with nonlinear Neumann boundary conditions [J]. Calc Var Partial Diff Equ,2008,32(4): 429-452.

      [2]BIDAUTVERON M F, PONCE A, VERON L. Boundary singularities of positive solutions of some nonlinear elliptic equations [J]. C R Acad Sci Paris Ser I Math, 2007,344(2): 83-88.

      [3]HU B. Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition [J]. Differential Integral Equations. 1994,7(2): 301-313.

      [4]MCKENNA P J, REICHEL W. A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains [J]. J Funct Anal, 2007,244(1) : 220-246.

      [5]PACARD F. Existence de solutions faibles positive de dans des ouverts bornes de [J]. C R Acad Sci Paris Ser. I Math, 1992,315(7) : 793-798.

      [6]PACARD F. Existence and convergence of positive weak solutions of in a bounded domains of [J]. Calc Var Partial Diff Equ, 1993, 1(3) : 243-265.

      [7]QUITTNER P, SOUPLET PH. A priori estimates and existence for elliptic systems via bootstrap in a weighted Lebesgue spaces [J]. Arch Ration Mech Anal, 2004, 174(1): 49-81.

      [8]CABRE X, SIRE Y. Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates [J]. Ann Inst H Poincar\'{e} Anal NonLin\'{e}aire, 2014,31(1) : 23-53.

      摘要:定義了在所謂的具有一片平的邊界的有界光滑區(qū)域內(nèi)退化線性橢圓的非常弱解的概念,然后利用變法方法與退化橢圓方程的極值原理等證明了該問(wèn)題非常弱解的存在唯一性結(jié)果.

      關(guān)鍵詞:存在性; 唯一性; 非常弱解; 退化橢圓方程

      中圖分類號(hào):O175.25 文獻(xiàn)標(biāo)識(shí)碼:A

      他們需要得到上面問(wèn)題非常弱解的存在唯一性結(jié)果.

      [1]QUITTNER P, REICHEL W. Very weak solutions to elliptic equations with nonlinear Neumann boundary conditions [J]. Calc Var Partial Diff Equ,2008,32(4): 429-452.

      [2]BIDAUTVERON M F, PONCE A, VERON L. Boundary singularities of positive solutions of some nonlinear elliptic equations [J]. C R Acad Sci Paris Ser I Math, 2007,344(2): 83-88.

      [3]HU B. Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition [J]. Differential Integral Equations. 1994,7(2): 301-313.

      [4]MCKENNA P J, REICHEL W. A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains [J]. J Funct Anal, 2007,244(1) : 220-246.

      [5]PACARD F. Existence de solutions faibles positive de dans des ouverts bornes de [J]. C R Acad Sci Paris Ser. I Math, 1992,315(7) : 793-798.

      [6]PACARD F. Existence and convergence of positive weak solutions of in a bounded domains of [J]. Calc Var Partial Diff Equ, 1993, 1(3) : 243-265.

      [7]QUITTNER P, SOUPLET PH. A priori estimates and existence for elliptic systems via bootstrap in a weighted Lebesgue spaces [J]. Arch Ration Mech Anal, 2004, 174(1): 49-81.

      [8]CABRE X, SIRE Y. Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates [J]. Ann Inst H Poincar\'{e} Anal NonLin\'{e}aire, 2014,31(1) : 23-53.

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