Abstract
We deal with the Cauchy problem associated to a class of quasilinear singular parabolic equations with L ∞ coefficients whose prototypes are the p-Laplacian (2N/(N + 1) < p < 2) and the porous medium equation (((N − 2)/N)+ < m < 1). We prove existence of and sharp pointwise estimates from above and from below for the fundamental solutions. Our results can be extended to general non-negative L 1 initial data.
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Ragnedda, F., Vernier Piro, S. & Vespri, V. Pointwise estimates for the fundamental solutions of a class of singular parabolic problems. JAMA 121, 235–253 (2013). https://doi.org/10.1007/s11854-013-0034-x
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DOI: https://doi.org/10.1007/s11854-013-0034-x