Existence of weak dual solutions to the fractional porous medium equation is shown on general infinite graphs via weighted estimates on the fractional Green function, with additional comparison and smoothing results on trees.
Phragm\`en-Lindel\"of type theorems for parabolic equations on infinite graphs
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abstract
We obtain the Phragm\`en-Lindel\"of principle on combinatorial infinite weighted graphs for the Cauchy problem associated to a certain class of parabolic equations with a variable density. We show that the hypothesis made on the density is optimal.
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math.AP 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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The fractional Porous Medium Equation on graphs
Existence of weak dual solutions to the fractional porous medium equation is shown on general infinite graphs via weighted estimates on the fractional Green function, with additional comparison and smoothing results on trees.