Fredholm theory for an elliptic differential operator defined on \begin{document}$ \mathbb{R}^n $\end{document} and acting on generalized Sobolev spaces
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DOI: 10.3934/cpaa.2020074
Abstract: We consider a spectral problem for an elliptic differential operator debined on \begin{document}$ \mathbb{R}^n $\end{document} and acting on the generalized Sobolev space \begin{document}$ W^{0, \chi}_p(\mathbb{R}^n) $\end{document} for \begin{document}$ 1 . We note that similar problems,… read more here.
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Classification of solutions to a system of \begin{document}$ n^{\rm th} $\end{document} order equations on \begin{document}$ \mathbb R^n $\end{document}
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DOI: 10.3934/cpaa.2020246
Abstract: This work concerns the distributional solutions of a conformally invariant system of \begin{document}$ n^{\rm th} $\end{document} -order elliptic equations on \begin{document}$ \mathbb R^n $\end{document} having exponential type nonlinearity. The system in question is a natural… read more here.
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Inverse acoustic scattering using high-order small-inclusion expansion of misfit function
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DOI: 10.3934/ipi.2018039
Abstract: This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems involving the identification of penetrable obstacles, whereby the featured data-misfit cost function \begin{document} $\mathbb{J}$ \end{document} is expanded in powers… read more here.
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