Zobrazeno 1 - 10
of 96
pro vyhledávání: '"Ilkka Holopainen"'
We prove existence results for entire graphical translators of the mean curvature flow (the so-called bowl solitons) on Cartan-Hadamard manifolds. We show that the asymptotic behaviour of entire solitons depends heavily on the curvature of the manifo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::256bc243d19707690af2f67ee59c81f1
http://hdl.handle.net/10138/356706
http://hdl.handle.net/10138/356706
Publikováno v:
Journal of Dynamics and Differential Equations.
We study the fourth order Schr\"odinger equation with mixed dispersion on an $N$-dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using the fact that there exists a Fourier transform on this space, we prov
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12f83f58217679c9ec97d7ad4d1376ed
https://doi.org/10.1007/s10884-022-10197-4
https://doi.org/10.1007/s10884-022-10197-4
Assuming that there exists a translating soliton $u_\infty$ with speed $C$ in a domain $\Omega$ and with prescribed contact angle on $\partial\Omega$, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a871ea2ca6e364ee0593ca3ea9634be
http://hdl.handle.net/10138/341934
http://hdl.handle.net/10138/341934
Publikováno v:
Mathematische Zeitschrift
We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature H in warped product manifolds M× ϱR. In the first part of the paper, we prove the existence of Killing graphs with prescribed boundary on geodesic balls und
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f5f4e9cb3a657e631dc16c20f9f226db
http://hdl.handle.net/10138/315035
http://hdl.handle.net/10138/315035
Autor:
Seppo Rickman, Ilkka Holopainen
Publikováno v:
The Journal of Fourier Analysis and Applications
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::10b82b72b202f0e9ffe586e3ff910b80
https://doi.org/10.1201/9780429332838-14
https://doi.org/10.1201/9780429332838-14
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative sectional curva
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::63c664be3f8f10f5037ee3b428ed5db0
http://hdl.handle.net/10138/312016
http://hdl.handle.net/10138/312016
Publikováno v:
Potential Analysis
Potential Analysis, 2017, 47 (4), pp.485-501. ⟨10.1007/s11118-017-9624-z⟩
Potential Analysis, Springer Verlag, 2017, 47 (4), pp.485-501. ⟨10.1007/s11118-017-9624-z⟩
Potential Analysis, 2017, 47 (4), pp.485-501. ⟨10.1007/s11118-017-9624-z⟩
Potential Analysis, Springer Verlag, 2017, 47 (4), pp.485-501. ⟨10.1007/s11118-017-9624-z⟩
We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold M of dimension n 2 for a large class of operators containing, in particular, the p-Laplacian and the minimal graph operator. We extend several existence results obtained for the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::52eb51b23313afe876ff004856f1c269
https://doi.org/10.1007/s11118-017-9624-z
https://doi.org/10.1007/s11118-017-9624-z
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds $N$. More precisely, given a suitable subset $L$ of the asymptotic boundary of $N$ and a suitable functi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a4939bec40f560df3f1d902c8673dd0
We study the asymptotic Dirichlet and Plateau problems on Cartan-Hadamard manifolds satisfying the so-called Strict Convexity (abbr. SC) condition. The main part of the paper consists in studying the SC condition on a manifold whose sectional curvatu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::174282aac23f4fc8a2d6471a33844b29
http://hdl.handle.net/10138/298273
http://hdl.handle.net/10138/298273
Autor:
Ilkka Holopainen
Publikováno v:
Advances in Calculus of Variations. 9:163-185
We construct, by modifying Borbély's example, a 3-dimensional Cartan–Hadamard manifold M, with sectional curvatures at most -1, such that the asymptotic Dirichlet problem for the p-Laplacian is not solvable for any p > 1.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9acdf9aef71513968c0cbb8ab3548dbc
https://doi.org/10.1515/acv-2014-0043
https://doi.org/10.1515/acv-2014-0043