Geodesic
A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations
Eurasian mathematical journal, Tome 4 (2013) no. 3, pp. 70-83

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We consider eigenvalue problems for general elliptic operators of arbitrary order subject to homogeneous boundary conditions on open subsets of the Euclidean $N$-dimensional space. We prove stability results for the dependence of the eigenvalues upon variation of the mass density and we prove a maximum principle for extremum problems related to mass density perturbations which preserve the total mass. 
@article{EMJ_2013_4_3_a6,
     author = {P. D. Lamberti and L. Provenzano},
     title = {A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations},
     journal = {Eurasian mathematical journal},
     pages = {70--83},
     publisher = {mathdoc},
     volume = {4},
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     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2013_4_3_a6/}
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P. D. Lamberti; L. Provenzano. A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations. Eurasian mathematical journal, Tome 4 (2013) no. 3, pp. 70-83. http://geodesic.mathdoc.fr/item/EMJ_2013_4_3_a6/