Suppose that D is a （N+1）-connected （0≤N≤∞）,bounded circular domain in the interior of theunit circle, O∈D and its boundary = <sub>j</sub>∈C<sub>μ</sub><sup>2</sup>（0...Suppose that D is a （N+1）-connected （0≤N≤∞）,bounded circular domain in the interior of theunit circle, O∈D and its boundary = <sub>j</sub>∈C<sub>μ</sub><sup>2</sup>（0【μ【1）, where <sub>j</sub> （j=1,…,N） are situated inside <sub>0</sub>={z;|z|=1}.Now we consider the nonlinear uniformly elliptic complex equation of first order in z-plane:W<sub> </sub> = F（z,W,W<sub>z</sub>）, F = Q<sub>1</sub>W<sub>2</sub>+ Q<sub>2</sub>W<sub> </sub>+A<sub>1</sub>W + A<sub>2</sub>W + A<sub>3</sub>,Q<sub>j</sub> = Q<sub>j</sub>（z,W,W<sub>z</sub>）, j=1,2, A<sub>j</sub>= A<sub>j</sub>（z,W）, j=1,2,3, z∈D, （1）and suppose that the equation （1） satisfies condition C, i. e.The function F（z,W, v） is continuous with respect to z ∈D, W ∈E and V ∈E (E is the展开更多
Let D be a （N+1）-connected domain with the boundary = <sub>j</sub>∈C<sub>μ</sub><sup>1</sup>（0【μ【1） , where <sub>j</sub>（j=0,1,…, N） are simple closed cur...Let D be a （N+1）-connected domain with the boundary = <sub>j</sub>∈C<sub>μ</sub><sup>1</sup>（0【μ【1） , where <sub>j</sub>（j=0,1,…, N） are simple closed curves and <sub>j</sub>（j=1,…,N） are situated inside <sub>0</sub>={|z| =1}, and z=0∈D, we consider the complex elliptic equation of first orderwhereProblem A: Find a continuously differentiable solution W（z） on D, which satisfies the boundary con-ditionwhere λ（t） , f （t）∈B<sub>p<sup>1</sup>/P</sub>,1（ ）→C（ ）, and these satisfy confition C;展开更多
Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub&g...Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub>,r<sub>2</sub>,…,r<sub>h</sub>} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x<sub>3</sub>= a<sub>3</sub>, …,x<sub>n</sub> = a<sub>n</sub>（n3） , we obtain a section domain G<sub>a</sub> in the x<sub>1</sub>x<sub>2</sub> plane. Let L<sub>a</sub> be the boundary of G<sub>a</sub>, and its center is writ-ten as 0<sub> </sub> = （0,0,α<sub>3</sub>,...,α<sub>n</sub>） .展开更多
文摘Suppose that D is a （N+1）-connected （0≤N≤∞）,bounded circular domain in the interior of theunit circle, O∈D and its boundary = <sub>j</sub>∈C<sub>μ</sub><sup>2</sup>（0【μ【1）, where <sub>j</sub> （j=1,…,N） are situated inside <sub>0</sub>={z;|z|=1}.Now we consider the nonlinear uniformly elliptic complex equation of first order in z-plane:W<sub> </sub> = F（z,W,W<sub>z</sub>）, F = Q<sub>1</sub>W<sub>2</sub>+ Q<sub>2</sub>W<sub> </sub>+A<sub>1</sub>W + A<sub>2</sub>W + A<sub>3</sub>,Q<sub>j</sub> = Q<sub>j</sub>（z,W,W<sub>z</sub>）, j=1,2, A<sub>j</sub>= A<sub>j</sub>（z,W）, j=1,2,3, z∈D, （1）and suppose that the equation （1） satisfies condition C, i. e.The function F（z,W, v） is continuous with respect to z ∈D, W ∈E and V ∈E (E is the
文摘Let D be a （N+1）-connected domain with the boundary = <sub>j</sub>∈C<sub>μ</sub><sup>1</sup>（0【μ【1） , where <sub>j</sub>（j=0,1,…, N） are simple closed curves and <sub>j</sub>（j=1,…,N） are situated inside <sub>0</sub>={|z| =1}, and z=0∈D, we consider the complex elliptic equation of first orderwhereProblem A: Find a continuously differentiable solution W（z） on D, which satisfies the boundary con-ditionwhere λ（t） , f （t）∈B<sub>p<sup>1</sup>/P</sub>,1（ ）→C（ ）, and these satisfy confition C;
文摘Let A. （R） be a real Clifford algebra and Gan open connected set in R<sup>n</sup> . By [1], the function with val-ues in A<sub>n</sub> （R） may be written aswhere B ={r<sub>1</sub>,r<sub>2</sub>,…,r<sub>h</sub>} {1,2,…,n}represent that from the sum for’lst and 2nd indi-sates respectively, and we have the following result.Theorem A Function f （x） with values in A. （R） is regular in G if and only ifLet G be the unit hyperball and L the unit hypersphere. Cutting G by the plane: x<sub>3</sub>= a<sub>3</sub>, …,x<sub>n</sub> = a<sub>n</sub>（n3） , we obtain a section domain G<sub>a</sub> in the x<sub>1</sub>x<sub>2</sub> plane. Let L<sub>a</sub> be the boundary of G<sub>a</sub>, and its center is writ-ten as 0<sub> </sub> = （0,0,α<sub>3</sub>,...,α<sub>n</sub>） .
