The heat equation with nonlinear generalized Robin boundary conditions |
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Authors: | Markus Biegert |
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Institution: | a University of Ulm, Institute of Applied Analysis, D-89069 Ulm, Germany b University of Puerto Rico, Department of Mathematics (Rio Piedras Campus), PO Box 23355, San Juan, PR 00931-3355, USA |
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Abstract: | Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H1-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))t?0 on L2(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has |
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Keywords: | 35K05 35K60 35D10 47H20 |
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