Nonnegative solutions of parabolic operators with low-order terms

L. Riahi, Campus Universitaire, Tunis, Tunisia

E. J. Qualitative Theory of Diff. Equ., No. 12. (2003), pp. 1-16.

Communicated by J. H. Wu. Appeared on 2003-06-24

Abstract: We develop the harmonic analysis approach for parabolic operator with one order term in the parabolic Kato class on $C^{1,1}$-cylindrical domain $\Omega$. We study the boundary behaviour of nonnegative solutions. Using these results, we prove the integral representation theorem and the existence of nontangential limits on the boundary of $\Omega$ for nonnegative solutions. These results extend some first ones proved for less general parabolic operators.

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