Results 261 to 270 of about 12,245,009 (305)
Some of the next articles are maybe not open access.
Theoretical and Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
1970
Let d(n) denote the number of positive divisors of the positive integer n. Let $$E(x) = \sum\limits_{n \leqslant x} {d(n) - x\log x - (2\gamma - 1)x,\,x \geqslant 1}$$ where γ is Euler’s constant. It is known, after Dirichlet, that $$ E(x) = 0({x^{{\frac{1}{2}}}}),\quad as\quad x \to \infty $$
openaire +1 more source
Let d(n) denote the number of positive divisors of the positive integer n. Let $$E(x) = \sum\limits_{n \leqslant x} {d(n) - x\log x - (2\gamma - 1)x,\,x \geqslant 1}$$ where γ is Euler’s constant. It is known, after Dirichlet, that $$ E(x) = 0({x^{{\frac{1}{2}}}}),\quad as\quad x \to \infty $$
openaire +1 more source
Dirichlet's problem in banach space
Mathematical Notes of the Academy of Sciences of the USSR, 1983The author investigates a Dirichlet problem for the equation \(Lu=tr A(x)u''(x)A(x)+u'(x)a(x)=-g(x)\) in a region G of a Banach space X with boundary \(\Gamma\). Using a known probability representation of the solution of the problem \(Lu=-g\), \(u|_{\Gamma}=\psi\) he extends some results by \textit{N. N. Frolov} [Teor. Veroyatn. Mat. Stat. 3, 200-210 (
openaire +2 more sources
On a Constrained Dirichlet Problem
SIAM Journal on Control and Optimization, 2002Summary: We consider a Dirichlet minimum problem with a pointwise constraint on the gradient, i.e., \(\| \nabla u(x)\| \leq 1\) a.e., or, equivalently, an unconstrained minimum problem with an extended-valued integrand. Since the subdifferential of this integrand is defined on the whole effective domain, the problem of the validity of the Euler ...
openaire +2 more sources
1991
This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3 ...
openaire +1 more source
This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3 ...
openaire +1 more source
1981
Da die Kugelfunktionen eine wichtige Rolle bei speziellen Problemen der Potentialtheorie spielen (vgl. z.B. [24],[30),[52]), bietet es sich an, als Anwendung des Transformationskalkuls die Laplace -Differentialgleichung ∆U =O zu untersuchen. Mit ∆ ist hier der ubliche dreidimensionale Laplace — Differentialoperator: $$ \Delta : = \frac{{{d^2 ...
openaire +1 more source
Da die Kugelfunktionen eine wichtige Rolle bei speziellen Problemen der Potentialtheorie spielen (vgl. z.B. [24],[30),[52]), bietet es sich an, als Anwendung des Transformationskalkuls die Laplace -Differentialgleichung ∆U =O zu untersuchen. Mit ∆ ist hier der ubliche dreidimensionale Laplace — Differentialoperator: $$ \Delta : = \frac{{{d^2 ...
openaire +1 more source
The Dirichlet problem for stable-like operators and related probabilistic representations
, 2016A. Arapostathis +2 more
semanticscholar +1 more source