Positive radial solutions for semilinear biharmonic equations in annular domains.
Under natural regularity assumptions on the data the powers of regular elliptic boundary value problems (e.b.v.p.) are shown to be higher order regular e.b.v.p.. This result is used in description of the domains of fractional powers of elliptic operators which information is in order important in regularity considerations for solutions of semilinear parabolic equations. Presented approach allows to avoid C∞-smoothness assumption on the data that is typical in many references.
We consider a sequence of multi-bubble solutions of the following fourth order equationwhere is a positive function, is a bounded and smooth domain in , and is a constant such that . We show that (after extracting a subsequence), for some positive integer , where is the area of the unit sphere in . Furthermore, we obtain the following sharp estimates for :where , and in . This yields a bound of solutions as converges to from below provided thatThe analytic work of...