Abstract
This is the necessary and sucient conditions to the regularity of solution of elliptic problems on nonsmooth domains in R3. I study a boundary value problem for elliptic partial dierential equation.I study the regularity of solution to the problem in non smooth domain. I obtain the necessary andsucient conditions of the problem to belong to Cm+2+:
Highlights
The regularities of the solutions on nonsmooth domains are typically described in terms of usual
In engineering applications many problems in R3 are characterized by partial differential equations with piecewise analytic data such as nonsmooth domains, abruptly changes of types of boundary conditions, piecewise analytic coefficients and boudary conditions, etc., for instance, the physical domains of structral mechanical problems often have edges and vertices, interfaces between di?erent materials and material cracks [13,14,15]
Comprehensive study on the regularity of the solutions of elliptic problems in R3 with piecewise analytic data is of great significance for theoretical reasons and for the desigh of effective computations and the optimal convergence of numerical method for these problems [16,17,18,19,20]
Summary
The regularities of the solutions on nonsmooth domains are typically described in terms of usual. In engineering applications many problems in R3 are characterized by partial differential equations with piecewise analytic data such as nonsmooth domains, abruptly changes of types of boundary conditions, piecewise analytic coefficients and boudary conditions, etc., for instance, the physical domains of structral mechanical problems often have edges and vertices, interfaces between di?erent materials and material cracks [13,14,15] The solutions of these problems have strong sin- gularities at the edges and vertices and around the cracks, which make the conventional numerical approximation extremely difficult and inefficient. By repeating this process we can extend the domain until the angle is π, with the boundary function belonging to Cm+2+α
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