Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Francesco Della Pietra"'
Publikováno v:
van den Berg, M, Della Pietra, F, di Blasio, G & Gavitone, N 2021, ' Efficiency and localisation for the first Dirichlet eigenfunction ', Journal of Spectral Theory, vol. 11, no. 3, pp. 981-1003 . https://doi.org/10.4171/JST/363
Bounds are obtained for the efficiency or mean to peak ratio $E(\Omega)$ for the first Dirichlet eigenfunction (positive) for open, connected sets $\Omega$ with finite measure in Euclidean space $\R^m$. It is shown that (i) localisation implies vanis
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::303923d39a6fd0b9feffa88e1ede3999
https://doi.org/10.4171/jst/363
https://doi.org/10.4171/jst/363
In this paper, we study the Γ-limit, as p → 1 {p\to 1} , of the functional J p ( u ) = ∫ Ω | ∇ u | p + β ∫ ∂ Ω | u | p ∫ Ω | u | p , J_{p}(u)=\frac{\int_{\Omega}\lvert\nabla u\rvert^{p}+\beta\int_{\partial\Omega% }\lv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18368eee04fd8cfcf33820476ce7de85
http://hdl.handle.net/11588/868395
http://hdl.handle.net/11588/868395
We study the asymptotic behaviour, as $p\to 1^+$ , of the solutions of the following inhomogeneous Robin boundary value problem: P \begin{equation*} \begin{cases} \displaystyle -\Delta_p u_p = f & \text{ in }\Omega,\\ \displaystyle |\nabla u_p|^{p-2}
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::314b45eb59ef004b5ee985adca7b4452
We study thermal insulating of a bounded body $\Omega\subset \mathbb{R}^n$. Under a prescribed heat source $f\geq 0$, we consider a model of heat transfer between $\Omega$ and the environment determined by convection; this corresponds, before insulat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78dcb91deacef8d12a428da4c7578a45
http://hdl.handle.net/11588/815492
http://hdl.handle.net/11588/815492
Let us consider the following minimum problem \[ \lambda_\alpha(p,r)= \min_{\substack{u\in W_{0}^{1,p}(-1,1)\\ u\not\equiv0}}\dfrac{\displaystyle\int_{-1}^{1}|u'|^{p}dx+\alpha\left|\int_{-1}^{1}|u|^{r-1}u\, dx\right|^{\frac pr}}{\displaystyle\int_{-1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::112ea1f04ad920cd67089959d6e2e6bb
http://hdl.handle.net/11588/804877
http://hdl.handle.net/11588/804877
In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for thep-Laplacian operator in domains with convex holes. An analogous estimate is obtained for the corresponding torsional rigidity prob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10c3e9452da263691e65c12a0f9736aa
https://hdl.handle.net/11367/117044
https://hdl.handle.net/11367/117044
Publikováno v:
Advances in Nonlinear Analysis, Vol 9, Iss 1, Pp 278-291 (2018)
In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λ F ( p , Ω ) {\lambda_{F}(p,\Omega)} of the anisotropic p-Laplacian, 1 < p < + ∞ {1 . Our aim is to enhance, by means of the 𝒫
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0c293419d635fb2ed5cbe7360a0a5e2
http://hdl.handle.net/11588/726524
http://hdl.handle.net/11588/726524
In this paper we consider a minimization problem which arises from thermal insulation. A compact connected set K, which represents a conductor of constant temperature, say 1, is thermally insulated by surrounding it with a layer of thermal insulator,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab12bffd97ddd5f24a0089ded4a0660e
Publikováno v:
Advances in Mathematics. 388:107887
In this paper we introduce new symmetrization with respect to mixed volume or anisotropic curvature integral, which generalizes the one with respect to quermassintegral due to Talenti and Tso. We show a P\'olya-Szego type principle for such symmetriz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc7db3b6e8a530be6661ae7272e4b2f6
https://doi.org/10.1016/j.aim.2021.107887
https://doi.org/10.1016/j.aim.2021.107887
Let Ω be a bounded open set of R n , n ≥ 2 . In this paper we mainly study some properties of the second Dirichlet eigenvalue λ 2 ( p , Ω ) of the anisotropic p-Laplacian − Q p u : = − div ( F p − 1 ( ∇ u ) F ξ ( ∇ u ) ) , where F is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd7dcd9591091f00fabfdd15db43e0bf
https://hdl.handle.net/11367/117051
https://hdl.handle.net/11367/117051