Zobrazeno 1 - 10
of 120
pro vyhledávání: '"Verbitsky, Igor E."'
Autor:
Verbitsky, Igor E.
We give a survey of nonlinear potential estimates and their applications obtained recently for positive solutions to sublinear problems of the type \[ u = \mathbf{G}(\sigma u^q) + f \quad \textrm{in} \,\, \Omega, \] where $0 < q < 1$, $\sigma\ge 0$ i
Externí odkaz:
http://arxiv.org/abs/2210.11008
Autor:
Phuc, Nguyen Cong, Verbitsky, Igor E.
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, \\ \displaystyle{\liminf_{|x|\rig
Externí odkaz:
http://arxiv.org/abs/2208.13272
Autor:
Verbitsky, Igor E.
We give bilateral pointwise estimates for positive solutions $u$ to the sublinear integral equation \[ u = \mathbf{G}(\sigma u^q) + f \quad \textrm{in} \,\, \Omega,\] for $0 < q < 1$, where $\sigma\ge 0$ is a measurable function, or a Radon measure,
Externí odkaz:
http://arxiv.org/abs/2203.02531
Autor:
Phuc, Nguyen Cong, Verbitsky, Igor E.
We give necessary and sufficient conditions for the existence of a BMO solution to the quasilinear equation $-\Delta_{p} u = \mu$ in $\mathbb{R}^n$, $u\ge 0$, where $\mu$ is a locally finite Radon measure, and $\Delta_{p}u= \text{div}(|\nabla u|^{p-2
Externí odkaz:
http://arxiv.org/abs/2105.05282
We give bilateral pointwise estimates for positive solutions of the equation \begin{equation*} \left\{ \begin{aligned} -\triangle u & = \omega u \, \,& & \mbox{in} \, \, \Omega, \quad u \ge 0, \\ u & = f \, \, & &\mbox{on} \, \, \partial \Omega , \en
Externí odkaz:
http://arxiv.org/abs/2011.04083
Autor:
Verbitsky, Igor E.
Publikováno v:
Atti Accad. Naz. Lincei Rend. Lincei, Mat. Appl. 30 (2019), no. 4, 733-758
We discuss recent advances in the theory of quasilinear equations of the type $ -\Delta_{p} u = \sigma u^{q} \; \; \text{in} \;\; \mathbb{R}^n, $ in the case $0
Externí odkaz:
http://arxiv.org/abs/1905.08121
Autor:
Verbitsky, Igor E.
We prove an analogue of Wolff's inequality for the so-called intrinsic nonlinear potentials associated with the quasilinear elliptic equation \[ -\Delta_{p} u = \sigma u^{q} \quad \text{in} \;\; \mathbb{R}^n, \] in the sub-natural growth case $0
Externí odkaz:
http://arxiv.org/abs/1812.03418
Autor:
Seesanea, Adisak, Verbitsky, Igor E.
We study the existence problem for positive solutions $u \in L^{r}(\mathbb{R}^{n})$, $0
Externí odkaz:
http://arxiv.org/abs/1811.10163
Autor:
Hänninen, Timo S., Verbitsky, Igor E.
Let $\sigma$ and $\omega$ be locally finite Borel measures on $\mathbb{R}^d$, and let $p\in(1,\infty)$ and $q\in(0,\infty)$. We study the two-weight norm inequality $$ \lVert T(f\sigma) \rVert_{L^q(\omega)}\leq C \lVert f \rVert_{L^p(\sigma)}, \quad
Externí odkaz:
http://arxiv.org/abs/1809.10800
Autor:
Seesanea, Adisak, Verbitsky, Igor E.
We give necessary and sufficient conditions for the existence of a positive solution with zero boundary values to the elliptic equation \[ \mathcal{L}u = \sigma u^{q} + \mu \quad \text{in} \;\; \Omega, \] in the sublinear case $0
Externí odkaz:
http://arxiv.org/abs/1804.09255