EXISTENCE AND REGULARITY OF WEAK SOLUTIONS FOR THE BIHARMONIC EQUATION WITH COMPLETE SECOND ORDER DERIVATIVE

摘要

In this paper, we discuss the biharmonic equations with complete second order derivative terms. We prove that the equation admits a unique weak solution under some conditions. Via some techniques and difference quotients method, we also show the interior regularity and the boundary regularity of the weak solution. These techniques include cutoff function, coordinate transposition, flatten out the boundary, finitely covered theorem, general Sobolev inequalities, interpolation inequality, etc.