Riemann-hilbert Boundary Value Problems For Meta-analytic Functions In Variable Exponent Spaces

Riemann-Hilbert boundary value problem for meta-analytic functions in variable exponent space is a kind of important boundary value problem in complex analysis,which has close relationship with electromagnetic problems,elasticity,fluid mechanics and other practical problems.In this thesis,we mainly discuss two kinds of boundary value problems of meta-analytic functions in variable exponent space,namely Riemann boundary value problem and Hilbert boundary value problem.The Riemann boundary value problems on a simple curve with the same factor or on a unit circle with two different factors and Hilbert boundary value problem of the meta-analytic functions with variable exponent space are solved.The explicit expressions and solvability conditions of the general solutions are obtained respectively.The meta-analytic function in variable exponent space is defined reasonably,and the decomposition theorem of meta-analytic function in variable exponent space is deduced by referring to the decomposition theorem of poly-analytic function,which is the basis and key of the whole thesis.The boundary value problem of meta-analytic functions in variable exponent space is proposed,including coefficients,conditions satisfied by boundary values and growth conditions,etc.The most suitable decomposition form is selected according to the specific boundary value problem,and the proposed boundary value problem of meta-analytic function is transformed into boundary value problem of analytic function or lower order meta-analytic function.After obtaining the solution of the boundary value problem of analytic function or lower order meta-analytic function according to relevant literatures,the explicit expression and solvability condition of the solution to the original boundary value problem are given by using decomposition theorem again.0 pictures,0 tables,60 references...