Abstract
Let \(\Omega \subset {R^3}\) be a bounded Lipshitz domain, and let \(\zeta \in {C^3},\zeta \cdot \zeta = 0.\) In Ω, consider an elliptic equation
with \(a \in {C^1}\left( {\bar \Omega } \right),b \in {L^\infty }\left( \Omega \right).\) Assume also that a is real valued and has a positive lower bound. We prove that for |ζ| sufficiently large, this equation has special quasi-exponential solutions of the form
depending on parameter ζ and such that \({\left\| \omega \right\|_{{L^2}\left( \Omega \right)}} = 0\left( {|\zeta {|^{ - \alpha }}} \right),\) for any α ∈ (0,1).
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Panchenko, A. (2000). Quasi-Exponential Solutions for Some PDE with Coefficients of Limited Regularity. In: Gilbert, R.P., Kajiwara, J., Xu, Y.S. (eds) Direct and Inverse Problems of Mathematical Physics. International Society for Analysis, Applications and Computation, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3214-6_9
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DOI: https://doi.org/10.1007/978-1-4757-3214-6_9
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