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pro vyhledávání: '"Bobkov, Vladimir A."'
Along with the partition of a planar bounded domain $\Omega$ by the nodal set of a fixed eigenfunction of the Laplace operator in $\Omega$, one can consider another natural partition of $\Omega$ by, roughly speaking, gradient flow lines of a special
Externí odkaz:
http://arxiv.org/abs/2410.07811
Autor:
Bobkov, Vladimir, Kolonitskii, Sergey
Let $u$ be either a second eigenfunction of the fractional $p$-Laplacian or a least energy nodal solution of the equation $(-\Delta)^s_p \, u = f(u)$ with superhomogeneous and subcritical nonlinearity $f$, in a bounded open set $\Omega$ and under the
Externí odkaz:
http://arxiv.org/abs/2405.06936
Let $\tau_k(\Omega)$ be the $k$-th eigenvalue of the Laplace operator in a bounded domain $\Omega$ of the form $\Omega_{\text{out}} \setminus \overline{B_{\alpha}}$ under the Neumann boundary condition on $\partial \Omega_{\text{out}}$ and the Robin
Externí odkaz:
http://arxiv.org/abs/2309.15558
Autor:
Bobkov, Vladimir, Tanaka, Mieko
We investigate the existence and multiplicity of abstract weak solutions of the equation $-\Delta_p u -\Delta_q u=\alpha |u|^{p-2}u + \beta |u|^{q-2}u$ in a bounded domain under zero Dirichlet boundary conditions, assuming $1
Externí odkaz:
http://arxiv.org/abs/2308.16581
We show that the parabolic equation $u_t + (-\Delta)^s u = q(x) |u|^{\alpha-1} u$ posed in a time-space cylinder $(0,T) \times \mathbb{R}^N$ and coupled with zero initial condition and zero nonlocal Dirichlet condition in $(0,T) \times (\mathbb{R}^N
Externí odkaz:
http://arxiv.org/abs/2302.06363
Autor:
Bobkov, Vladimir, Kolonitskii, Sergey
For a smooth bounded domain $\Omega$ and $p \geq q \geq 2$, we establish quantified versions of the classical Friedrichs inequality $\|\nabla u\|_p^p - \lambda_1 \|u\|_q^p \geq 0$, $u \in W_0^{1,p}(\Omega)$, where $\lambda_1$ is a generalized least f
Externí odkaz:
http://arxiv.org/abs/2210.14111
Autor:
Bobkov, Vladimir, Tanaka, Mieko
We investigate qualitative properties of weak solutions of the Dirichlet problem for the equation $-\Delta_p u = \lambda m(x)|u|^{p-2}u + \eta a(x)|u|^{q-2}u + f(x)$ in a bounded domain $\Omega \subset \mathbb{R}^N$, where $q
Externí odkaz:
http://arxiv.org/abs/2210.08898
Autor:
Baustian, Falko, Bobkov, Vladimir
We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,\pi)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we
Externí odkaz:
http://arxiv.org/abs/2204.06244
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 December 2024 540(2)
Autor:
Baustian, Falko, Bobkov, Vladimir
We provide improved sufficient assumptions on sequences of Fucik eigenvalues of the one-dimensional Dirichlet Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,\pi)$. For that purpose, we introduce a c
Externí odkaz:
http://arxiv.org/abs/2111.08329