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The rate of growth of the energy integral of a quasiregular mapping $f 𝒳 \to 𝒴$ is estimated in terms of a special isoperimetric condition on $𝒴$ . The estimate leads to new Phragmén-Lindelöf type theorems.

Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization.

F. Chiacchio (2009)

Publicacions Matemàtiques

Estimates for the Green function and characterization of a certain Kato class by the Gauss semigroup in the half space.

Bachar, Imed (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Estimates for the Green function and existence of positive solutions for higher-order elliptic equations.

Bachar, Imed (2006)

Abstract and Applied Analysis

Estimates for the Green function and singular solutions for polyharmonic nonlinear equation.

Bachar, Imed, Màagli, Habib, Masmoudi, Syrine, Zribi, Malek (2003)

Abstract and Applied Analysis

Estimates for the multiplicative square function of solutions to nondivergence elliptic equations.

Rivera-Noriega, Jorge (2007)

Abstract and Applied Analysis

Estimates for the parametrix of the Kohn Laplacian on certain domains.

Matei Machedon (1988)

Inventiones mathematicae

Estimates from above and from below for the Homogenized Coefficients.

Luisa Donatella Marini (1986/1987)

Numerische Mathematik

Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation

Vladimir A. Kondratiev, Olga A. Oleinik (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Per ogni soluzione della (1) nel dominio limitato $\Omega$ ,, appartenente a $H_{0}^{2}(\Omega)$ e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto $x^{0}$ del contorno; si consente a $\partial\Omega$ di essere singolare in $x^{0}$ .

Estimates of eigenvalues and eigenfunctions in periodic homogenization

Carlos E. Kenig, Fanghua Lin, Zhongwei Shen (2013)

Journal of the European Mathematical Society

For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an $O (ϵ)$ estimate in $H^{1}$ for solutions with Dirichlet condition.

Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms.

Abdoul Ifra, Lofti Riahi (2005)

Publicacions Matemàtiques

Estimates of solutions to linear elliptic systems and equations

Heinrich Begehr (1992)

Banach Center Publications

Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized first order Beltrami systems in the plane and for second order elliptic equations in $ℝ^{m}$ . Different types of boundary value problems are considered. For Beltrami systems these are the Riemann-Hilbert, the Riemann and the Poincaré problem, while for elliptic...

Estimates of the principal eigenvalue of the $p$ -Laplacian and the $p$ -biharmonic operator

Jiří Benedikt (2015)

Mathematica Bohemica

We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet $p$ -Laplacian and the Navier $p$ -biharmonic operator on a ball of radius $R$ in $ℝ^{N}$ and its asymptotics for $p$ approaching $1$ and $\infty$ . Let $p$ tend to $\infty$ . There is a critical radius $R_{C}$ of the ball such that the principal eigenvalue goes to $\infty$ for $0 < R \leq R_{C}$ and to $0$ for $R > R_{C}$ . The critical radius is $R_{C} = 1$ for any $N \in ℕ$ for the $p$ -Laplacian and $R_{C} = \sqrt{2 N}$ in the case of the $p$ -biharmonic operator. When $p$ approaches $1$ , the principal eigenvalue of the Dirichlet...

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