Monotonicity of a parabolic frequency function yields backward uniqueness for q(p-1) >= 1 and Liouville-type results for ancient solutions of doubly nonlinear equations on manifolds.
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The Cauchy problem for ∂t u = Δp u^q on Riemannian manifolds admits a unique weak solution when p>1, q>0, pq≥1 for any initial data in L1(M) ∩ L∞(M).
A certain upper bound for weak solutions of the Leibenson equation on Riemannian manifolds is equivalent to a Euclidean-type Sobolev inequality.
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Parabolic Frequency for Doubly Nonlinear Equations on Manifolds
Monotonicity of a parabolic frequency function yields backward uniqueness for q(p-1) >= 1 and Liouville-type results for ancient solutions of doubly nonlinear equations on manifolds.
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Existence results for Leibenson's equation on Riemannian manifolds
The Cauchy problem for ∂t u = Δp u^q on Riemannian manifolds admits a unique weak solution when p>1, q>0, pq≥1 for any initial data in L1(M) ∩ L∞(M).
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Long time upper bounds for solutions of Leibenson's equation on Riemannian manifolds
A certain upper bound for weak solutions of the Leibenson equation on Riemannian manifolds is equivalent to a Euclidean-type Sobolev inequality.