Harnack’s inequality for doubly nonlinear equations of slow diffusion type
2021 ◽
Vol 60
(6)
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Keyword(s):
AbstractIn this article we prove a Harnack inequality for non-negative weak solutions to doubly nonlinear parabolic equations of the form $$\begin{aligned} \partial _t u - {{\,\mathrm{div}\,}}{\mathbf {A}}(x,t,u,Du^m) = {{\,\mathrm{div}\,}}F, \end{aligned}$$ ∂ t u - div A ( x , t , u , D u m ) = div F , where the vector field $${\mathbf {A}}$$ A fulfills p-ellipticity and growth conditions. We treat the slow diffusion case in its full range, i.e. all exponents $$m > 0$$ m > 0 and $$p>1$$ p > 1 with $$m(p-1) > 1$$ m ( p - 1 ) > 1 are included in our considerations.
2012 ◽
Vol 12
(4)
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pp. 1527-1546
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1967 ◽
Vol 3
(2)
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pp. 211-241
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1999 ◽
Vol 51
(7)
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pp. 996-1012
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2011 ◽
Vol 192
(2)
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pp. 273-296
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2011 ◽
Vol 63
(5)
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pp. 709-728
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