Geodesic
On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces
Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 909-917

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For linear differential operators with coefficients of class $C$ on $\mathbb R^n$, we prove theorems on the simultaneous invertibility and equivalence of spectra in the Lebesgue space $L^p$, Stepanov space $M^p$, and in a particular Banach space $V^p\subset L^p$, $p\ge 1$. 
@article{MZM_2002_72_6_a10,
     author = {V. M. Tyurin},
     title = {On the {Equivalence} of {Spectra} of {Linear} {Partial} {Differential} {Operators} in {Certain} {Function} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {909--917},
     publisher = {mathdoc},
     volume = {72},
     number = {6},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a10/}
}
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V. M. Tyurin. On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces. Matematičeskie zametki, Tome 72 (2002) no. 6, pp. 909-917. http://geodesic.mathdoc.fr/item/MZM_2002_72_6_a10/