A remark on the uniqueness of fundamental solutions to the -Laplacian equation, .
Laurençot, Ph. (1998)
Portugaliae Mathematica
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Laurençot, Ph. (1998)
Portugaliae Mathematica
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Jarmila Ranošová (1994)
Commentationes Mathematicae Universitatis Carolinae
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We characterize all subsets of such that for every bounded parabolic function on . The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated. ...
Ghanmi, Abdeljabbar, Toumi, Faten (2011)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Pavel Krejčí, Lucia Panizzi (2011)
Applications of Mathematics
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Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.