EUDML

Currently displaying 1 – 9 of 9

Order by Relevance | Title | Year of publication

Construction of the solutions of boundary value problems for the biharmonic operator in a rectangle

Nachman Aronszajn; R. D. Brown; R. S. Butcher — 1973

Annales de l'institut Fourier

A technique is developed for constructing the solution of $Δ^{2} u = F$ in $R = {(x, y) : | x | < a, | y | < b}$ , subject to boundary conditions $u = φ$ , $\frac{\partial u}{\partial n} = ψ$ on $\partial R$ . The problem is reduced to that of finding the orthogonal projection $P w$ of $w$ in $L^{2} (R)$ onto the subspace $H$ of square integrable functions harmonic in $R$ . This problem is solved by decomposition $H$ into the closed direct (not orthogonal) sum of two subspaces $H^{(1)}, H^{(2)}$ for which complete orthogonal bases are known. $P$ is expressed in terms of the projections $P^{(1)}$ , $P^{(2)}$ of $L^{2} (R)$ onto $H^{(1)}$ , $H^{(2)}$ respectively. The resulting construction...

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 9 of 9

Construction of the solutions of boundary value problems for the biharmonic operator in a rectangle

The distribution and moments of the error term in the Dirichlet divisor problem

The density of rational points on cubic surfaces

Acknowledgment of priority

A mean value estimate for real character sums

Fractional moments of Dirichlet L-functions

Square-free values of n² + 1

Convexity bounds for L-functions

A note on the fourth moment of Dirichlet L-functions