A two-parameter family of Harnack type inequalities for non-negative solutions of a class of singular, quasilinear, homogeneous parabolic equations is established, and it is shown that such estimates imply the Hoelder continuity of solutions. These classes of singular equations include p-Laplacean type equation in the sub-critical range 1<p\le\frac2N/(N+1) and equations of the porous medium type in the sub-critical range 0<m\le(N-2)_+/N.
Harnack Type Estimates and Hölder Continuity for Non-Negative Solutions to Certain Sub-Critically Singular Parabolic Partial Differential Equations
GIANAZZA, UGO PIETRO;
2010-01-01
Abstract
A two-parameter family of Harnack type inequalities for non-negative solutions of a class of singular, quasilinear, homogeneous parabolic equations is established, and it is shown that such estimates imply the Hoelder continuity of solutions. These classes of singular equations include p-Laplacean type equation in the sub-critical range 1File in questo prodotto:
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