Zobrazeno 1 - 10
of 114
pro vyhledávání: '"E. Verbitsky"'
Autor:
Nguyen Cong Phuc, Igor E. Verbitsky
Publikováno v:
Mathematics in Engineering, Vol 5, Iss 3, Pp 1-33 (2023)
We prove the uniqueness property for a class of entire solutions to the equation $ \begin{equation*} \left\{ \begin{array}{ll} -{\rm div}\, \mathcal{A}(x,\nabla u) = \sigma, \quad u\geq 0 \quad {\text{in }} \mathbb{R}^n, \\ {\liminf\limits_{|x|\r
Externí odkaz:
https://doaj.org/article/0c95eb586adb4177b446869e910c7c29
Autor:
Nguyen Cong Phuc, Igor E. Verbitsky
Publikováno v:
Annales de l'Institut Fourier. 72:1911-1939
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51c5c04f368551b4edc63b18234fa5bd
https://doi.org/10.5802/aif.3485
https://doi.org/10.5802/aif.3485
Autor:
Michael Frazier, Igor E. Verbitsky
Publikováno v:
The Journal of Geometric Analysis. 31:9016-9044
Let $$\Omega \subseteq \mathbb {R}^n$$ be an open set, where $$n \ge 2$$ . Suppose $$\omega $$ is a locally finite Borel measure on $$\Omega $$ . For $$\alpha \in (0,2)$$ , define the fractional Laplacian $$(-\triangle )^{\alpha /2}$$ via the Fourier
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b48fd1cdb0eb99465121e22085bc77c5
https://doi.org/10.1007/s12220-020-00576-y
https://doi.org/10.1007/s12220-020-00576-y
Autor:
I. E. Verbitsky, A. Seesanea
Publikováno v:
St Petersburg Mathematical Journal. 31(3):557-572
The paper is devoted to the existence problem for positive solutions u is an element of L-r(R-n), 0 < r < infinity, to the quasilinear elliptic equation -Delta(p)u = sigma u(q) in R-n in the subnatural growth case 0 < q < p - 1, where Delta(p)u = div
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2674c89ebdc9811630686ad8f803c714
http://hdl.handle.net/2115/78730
http://hdl.handle.net/2115/78730
Publikováno v:
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :721-750
We study pointwise behavior of positive solutions to nonlinear integral equations, and related inequalities, of the type \begin{equation*} u(x) - \int_\Omega G(x, y) \, g(u(y)) d \sigma (y) = h, \end{equation*} where $(\Omega, \sigma)$ is a locally c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1c5954de697280b9b16596a79c11b4c8
https://doi.org/10.2422/2036-2145.201802_011
https://doi.org/10.2422/2036-2145.201802_011
Autor:
Igor E. Verbitsky, Timo S. Hänninen
Publikováno v:
Indiana University Mathematics Journal. 69:837-871
Let $\sigma$, $\omega$ be measures on $\mathbb{R}^d$, and let $\{\lambda_Q\}_{Q\in\mathcal{D}}$ be a family of non-negative reals indexed by the collection $\mathcal{D}$ of dyadic cubes in $\mathbb{R}^d$. We characterize the two-weight norm inequalit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e650010f9b07cd86c9178f1f335f316c
https://doi.org/10.1512/iumj.2020.69.7893
https://doi.org/10.1512/iumj.2020.69.7893
Autor:
Igor E. Verbitsky, Vladimir Maz'ya
Publikováno v:
Acta Mathematica Sinica, English Series. 35:832-852
For the general second order linear differential operator with complex-valued distributional coefficients a(j,k), b(j), and c in an open set (n) (n 1), we present conditions which ensure that -L0 i ...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::291c71f90cf1fd0ebf20373b9fb023f4
https://doi.org/10.1007/s10114-019-8127-9
https://doi.org/10.1007/s10114-019-8127-9
Publikováno v:
Journal d'Analyse Mathématique. 137:559-601
We obtain sharp pointwise estimates for positive solutions to the equation $-Lu+Vu^q=f$, where $L$ is an elliptic operator in divergence form, $q\in\mathbb{R}\setminus \{0\}$, $f\geq 0$ and $V$ is a function that may change sign, in a domain $\Omega$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b5821c99b04e70997372359d2c7dc15
https://doi.org/10.1007/s11854-019-0004-z
https://doi.org/10.1007/s11854-019-0004-z
Let $M$ be a complete non-compact Riemannian manifold and let $\sigma $ be a Radon measure on $M$. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequaliy \begin{equation*} -\Delta u\geq \sigma u^{q
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9974ee18e7425bcdb853525f4d339641
https://pub.uni-bielefeld.de/record/2941868
https://pub.uni-bielefeld.de/record/2941868
Autor:
Michael Frazier, Igor E. Verbitsky
Publikováno v:
Annales de l’institut Fourier. 67:1393-1425
Let $\Omega \subset \mathbb{R}^n$, for $n \geq 2$, be a bounded $C^2$ domain. Let $q \in L^1_{loc} (\Omega)$ with $q \geq 0$. We give necessary conditions and matching sufficient conditions, which differ only in the constants involved, for the existe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::597c4c8f2b9d1e8a2ce1f3cb2193ab50
https://doi.org/10.5802/aif.3113
https://doi.org/10.5802/aif.3113