Two distinct critical exponents control the existence of weak solutions to the biharmonic heat equation with Hardy-Rellich potential and weighted nonlinearity in exterior domains.
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A critical exponent p_crit(α,N,λ) governs existence of classical solutions for p below it and nonexistence of weak solutions for p above it in the semilinear heat inequality with Hardy potential on the sphere.
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Double Criticality for a Hardy-Rellich Biharmonic Heat Equation in an Exterior Domain
Two distinct critical exponents control the existence of weak solutions to the biharmonic heat equation with Hardy-Rellich potential and weighted nonlinearity in exterior domains.
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Semilinear Heat Inequalities with a Hardy-Type Potential in an Exterior Geodesic Domain on $\mathbb{S}^N$
A critical exponent p_crit(α,N,λ) governs existence of classical solutions for p below it and nonexistence of weak solutions for p above it in the semilinear heat inequality with Hardy potential on the sphere.