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Continuous dependence on the boundary conditions for the Wentzell Laplacian

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Abstract

The solution u of the well-posed problem

$$\left\{\begin{array}{l@{\quad}l}\frac{\partial u}{\partial t}=\sum_{i,j=1}^{N}\partial_{i}(a_{ij}(x)\partial_{j}u),&(x,t)\in\Omega\times[0,+\infty),\\[2mm]u(x,0)=f(x),&x\in\Omega,\\[2mm]\sum_{i,j=1}^{N}\partial_{i}(a_{ij}(x)\partial_{j}u)+\beta (x)\sum_{i,j=1}^{N}a_{ij}(x)\partial_{j}un_{i}\\[1mm]\quad+\gamma(x)u-q\beta(x)\Delta_{LB}u=0,&(x,t)\in \partial\Omega\times[0,+\infty),\end{array}\right.$$

depends continuously on (a ij ,β,γ,q).

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Bari, Via E. Orabona 4, 70125, Bari, Italy

    Giuseppe Maria Coclite & Silvia Romanelli

  2. Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40126, Bologna, Italy

    Angelo Favini

  3. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Gisèle Ruiz Goldstein & Jerome A. Goldstein

Authors
  1. Giuseppe Maria Coclite
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  2. Angelo Favini
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  3. Gisèle Ruiz Goldstein
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  4. Jerome A. Goldstein
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  5. Silvia Romanelli
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Corresponding author

Correspondence to Giuseppe Maria Coclite.

Additional information

Communicated by Jimmie D. Lawson.

Dedicated to Karl H. Hofmann on his 75th birthday.

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Coclite, G.M., Favini, A., Goldstein, G.R. et al. Continuous dependence on the boundary conditions for the Wentzell Laplacian. Semigroup Forum 77, 101–108 (2008). https://doi.org/10.1007/s00233-008-9068-2

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  • DOI: https://doi.org/10.1007/s00233-008-9068-2

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