Abstract
The Dirichlet problem in a conical domain for some elliptic equations can be reduced by separation of variables to a linear abstract differential equation of first or second order in a Hubert space H. We review some results giving the solution u as a superposition of exponential H-valued polynomials \( {e^{{ - {\lambda_k}t}}}{p_k}(t) \).
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© 1996 Birkhäuser Boston
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Geymonat, G., Tcha-Kondor, O. (1996). Constructive Methods for Abstract Differential Equations and Applications. In: Cea, J., Chenais, D., Geymonat, G., Lions, J.L. (eds) Partial Differential Equations and Functional Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 22. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2436-5_11
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DOI: https://doi.org/10.1007/978-1-4612-2436-5_11
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