Boundedness for Some Doubly Nonlinear Parabolic Equations in Measure Spaces

Laleoglu, Rojbin

doi:10.1007/s10884-017-9585-3

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2023

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Cited by 5 publications

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“…(1.1). The doubly nonlinear case is not yet totally understood, although many results are available (see, for instance [32][33][34][37][38][39] and [40]). The case m + p = 3, the so called Trudinger's equation, is still object of intensive studies (see, for instance [42]).…”

Section: Introductionmentioning

confidence: 99%

Regularity results for a class of doubly nonlinear very singular parabolic equations

Fornaro

Vespri

2021

Nonlinear Analysis

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Section: Introductionmentioning

confidence: 99%

Regularity results for a class of doubly nonlinear very singular parabolic equations

Fornaro

Vespri

2021

Nonlinear Analysis

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Stability to a class of doubly nonlinear very singular parabolic equations

Fornaro

Vespri

2021

manuscripta math.

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A comparison principle for doubly nonlinear parabolic partial differential equations

Bögelein,

Strunk

2023

Annali di Matematica

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In this paper, we derive a comparison principle for non-negative weak sub- and super-solutions to doubly nonlinear parabolic partial differential equations whose prototype is $$\begin{aligned} \partial _t u^q - {{\,\textrm{div}\,}}{\big (|\nabla u|^{p-2}\nabla u \big )}=0 \qquad \text{ in } \Omega _T, \end{aligned}$$ ∂ t u q - div ( | ∇ u | p - 2 ∇ u ) = 0 in Ω T , with $$q>0$$ q > 0 and $$p>1$$ p > 1 and $$\Omega _T:=\Omega \times (0,T)\subset \mathbb {R}^{n+1}$$ Ω T : = Ω × ( 0 , T ) ⊂ R n + 1 . Instead of requiring a lower bound for the sub- or super-solutions in the whole domain $$\Omega _T$$ Ω T , we only assume the lateral boundary data to be strictly positive. The main results yield some applications. Firstly, we obtain uniqueness of non-negative weak solutions to the associated Cauchy–Dirichlet problem. Secondly, we prove that any weak solution is also a viscosity solution.

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Boundedness for Some Doubly Nonlinear Parabolic Equations in Measure Spaces

Cited by 5 publications

References 17 publications

Regularity results for a class of doubly nonlinear very singular parabolic equations

Regularity results for a class of doubly nonlinear very singular parabolic equations

Stability to a class of doubly nonlinear very singular parabolic equations

A comparison principle for doubly nonlinear parabolic partial differential equations

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