Abstract
In this work, we study an elliptic differential equation set in three habitats with skewness boundary conditions at the interfaces. It represents the linear stationary case of dispersal problems of population dynamics which incorporate responses at interfaces between the habitats. Existence, uniqueness and regularity of the solution of these problems are obtained in Hölder spaces under necessary and sufficient conditions on the data. Our techniques are based on the semigroup theory, the fractional powers of linear operators, the \(H^{\infty }\) functional calculus for sectorial operators in Banach spaces and some properties of real interpolation spaces.
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Labbas, R., Medeghri, A. & Menad, A. Solvability of Elliptic Differential Equations, Set in Three Habitats with Skewness Boundary Conditions at the Interfaces. Mediterr. J. Math. 15, 128 (2018). https://doi.org/10.1007/s00009-018-1177-x
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DOI: https://doi.org/10.1007/s00009-018-1177-x