Equivalence of viscosity and weak solutions for a p-parabolic equation
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AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p>1$$ p > 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .
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1983 ◽
Vol 41
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pp. 194-195
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1970 ◽
Vol 28
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pp. 156-157
1991 ◽
Vol 49
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pp. 236-237
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1985 ◽
Vol 49
(4)
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pp. 207-213
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1985 ◽
Vol 49
(8)
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pp. 573-578
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1993 ◽
Vol 2
(3)
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pp. 52-55
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