Estimates of the negative spectrum of an elliptic operator

1992 ◽  
pp. 111-140 ◽  
Author(s):  
Yu. V. Egorov ◽  
V. A. Kondrat′ev
Keyword(s):  
Elliptic Operator ◽  
Negative Spectrum

ON THE NEGATIVE SPECTRUM OF AN ELLIPTIC OPERATOR

1991 ◽  
Vol 69 (1) ◽  
pp. 155-177 ◽  
Author(s):  
Yurii V Egorov ◽  
V A Kondrat'ev
Keyword(s):  
Elliptic Operator ◽  
Negative Spectrum

On the negative spectrum of an elliptic operator

2010 ◽  
Vol 81 (1) ◽  
pp. 28-30
Author(s):  
R. V. Guseinov
Keyword(s):  
Elliptic Operator ◽  
Negative Spectrum

Partial avaraging of the nondivergence second order elliptic operator

2016 ◽  
Vol 31 (3) ◽  
pp. 47-53
Author(s):  
M.M. Sirazhudinov ◽  
◽  
S.P. Dzhamaludinova ◽  
M.E. Mahmudova ◽  
◽  
...  
Keyword(s):  
Elliptic Operator ◽  
Second Order ◽  
Order Elliptic Operator

scholarly journals Quasilinear Riccati-Type Equations with Oscillatory and Singular Data

2020 ◽  
Vol 20 (2) ◽  
pp. 373-384
Author(s):  
Quoc-Hung Nguyen ◽  
Nguyen Cong Phuc
Keyword(s):  
Elliptic Operator ◽  
Bounded Domain ◽  
Existence Of Solutions ◽  
Type Equation ◽  
Linear Range ◽  
Measure Data ◽  
Regularity Conditions ◽  
Compactly Supported ◽  
Singular Data ◽  
Quasilinear Elliptic

AbstractWe characterize the existence of solutions to the quasilinear Riccati-type equation\left\{\begin{aligned} \displaystyle-\operatorname{div}\mathcal{A}(x,\nabla u)% &\displaystyle=|\nabla u|^{q}+\sigma&&\displaystyle\phantom{}\text{in }\Omega,% \\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{on }\partial% \Omega,\end{aligned}\right.with a distributional or measure datum σ. Here {\operatorname{div}\mathcal{A}(x,\nabla u)} is a quasilinear elliptic operator modeled after the p-Laplacian ({p>1}), and Ω is a bounded domain whose boundary is sufficiently flat (in the sense of Reifenberg). For distributional data, we assume that {p>1} and {q>p}. For measure data, we assume that they are compactly supported in Ω, {p>\frac{3n-2}{2n-1}}, and q is in the sub-linear range {p-1<q<1}. We also assume more regularity conditions on {\mathcal{A}} and on {\partial\Omega\Omega} in this case.

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

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