...y and sufficient conditions for the solvability of the [[Dirichlet problem|Dirichlet problem]] in appropriate Nikol'skii spaces in terms of membership of the bo
then the [[Dirichlet integral|Dirichlet integral]] $ D ( u) $
11 KB (1,572 words) - 19:46, 12 January 2024
.../b/b015/b015110/b01511034.png" /> serves to write down the solution of the
Dirichlet problem as the so-called formula of de la Vallée-Poussin:
...015110/b01511043.png" /> to its boundary, and which reduces to solving the
Dirichlet problem for a sufficiently smooth domain <img align="absmiddle" border="0"
21 KB (2,931 words) - 16:56, 7 February 2011
...more remote from that point than from all other points in the system. The Dirichlet domains of the points of an $(r,R)$-system $\epsilon$ have pairwise no comm
...tively. Voronoi also showed that the most general (i.e. not necessarily of Dirichlet type) normal partitioning of $E^n$ into identical convex, parallel polyhedr
8 KB (1,201 words) - 19:28, 2 June 2016
...bounds for the number $N(\sigma,T,\chi)$ of zeros $\rho=\beta+i\gamma$ of Dirichlet $L$-functions
...unds are substantially supplemented by results on the absence of zeros for Dirichlet $L$-functions in neighbourhoods of the straight line $\sigma=1$, obtained u
3 KB (519 words) - 11:35, 26 March 2023
At every point $x$, the Dirichlet formula
is the [[Dirichlet kernel|Dirichlet kernel]] of order $n$. This formula plays a key role in many problems in th
6 KB (1,047 words) - 11:37, 13 February 2024
that is a solution of the [[Dirichlet problem|Dirichlet problem]] for a domain $ D $
3 KB (486 words) - 01:08, 19 March 2022
...the methods used to attack it, the circle problem is largely analogous to Dirichlet's divisor problem (see [[Divisor problems|Divisor problems]]). A generaliza
5 KB (755 words) - 16:44, 4 June 2020
...heory of prime ends and boundary properties of plane mappings with bounded Dirichlet integrals" , Kiev (1981) (In Russian)</TD></TR><TR><TD valign="top">[8]</
...</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> M. Ohtsuka, "Dirichlet problem, extremal length and prime ends" , v. Nostrand-Reinhold (1970)</TD
4 KB (564 words) - 21:51, 16 December 2020
which has a unique solution of the [[Dirichlet problem|Dirichlet problem]] for any continuous boundary function . If the sequence of solutio
3 KB (513 words) - 17:09, 14 February 2020
...)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> R. Courant, "Dirichlet's principle, conformal mapping, and minimal surfaces" , Interscience (1950
4 KB (668 words) - 06:30, 31 March 2023
...maximum/minimum principle; and the solvability of the [[Dirichlet problem|Dirichlet problem]] for a sufficiently broad class of open sets in $ X $.
of the Dirichlet problem for $ U $
7 KB (1,087 words) - 19:43, 5 June 2020
is the conjugate [[Dirichlet kernel|Dirichlet kernel]]. If $ f $
4 KB (585 words) - 17:46, 4 June 2020
...Dirichlet boundary value problem (cf. also [[Dirichlet boundary conditions|Dirichlet boundary conditions]]):
...is bounded and the boundary $\partial \Omega$ is sufficiently regular, the Dirichlet Laplacian has a discrete spectrum of infinitely many positive eigenvalues w
12 KB (1,753 words) - 10:12, 16 March 2023
...rinciple (the Thue–Siegel lemma, cf. also [[Transcendency, measure of]]; [[Dirichlet principle]]). A clever computation of a determinant is an essential tool of
5 KB (726 words) - 09:23, 20 December 2014
Not all number fields are monogenic: Dirichlet gave the example of the [[cubic field]] generated by a root of the polynomi
1 KB (180 words) - 16:57, 25 November 2023
...eded in showing that if certain theorems concerning [[Dirichlet L-function|Dirichlet $L$-functions]] (which have not been proved till now) are valid, then any s
3 KB (514 words) - 21:14, 9 January 2015
Dirichlet kernels (cf. [[Dirichlet kernel|Dirichlet kernel]])
6 KB (837 words) - 08:14, 6 June 2020
...ation of the Dirichlet pigeon-hole principle (or [[Dirichlet box principle|Dirichlet box principle]]).
5 KB (836 words) - 14:32, 21 November 2016
Suppose, e.g., that one has to prove the solvability in a Hölder class of the Dirichlet problem
and considers for it the Dirichlet problem
9 KB (1,325 words) - 17:26, 7 February 2011
...n="top"> I.G. Petrovskii, "New existence proofs for the solution of the Dirichlet problem by the method of finite differences" ''Uspekhi Mat. Nauk'' , '''8'
9 KB (1,311 words) - 20:44, 29 January 2020