Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Prashanta Garain"'
Autor:
Prashanta Garain, Kaj Nyström
Publikováno v:
Mathematics in Engineering, Vol 5, Iss 2, Pp 1-37 (2023)
We consider nonlinear Kolmogorov-Fokker-Planck type equations of the form $ \begin{equation*} (\partial_t+X\cdot\nabla_Y)u = \nabla_X\cdot(A(\nabla_X u, X, Y, t)). \end{equation*} $ The function $ A = A(\xi, X, Y, t): \mathbb R^m\times \mathbb R^
Externí odkaz:
https://doaj.org/article/d1b4195e971b44edbb30035bb7de6ec3
Autor:
Prashanta Garain
Publikováno v:
Opuscula Mathematica, Vol 40, Iss 4, Pp 483-494 (2020)
In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by \[-\text{div}\big(w|\nabla u|^{p-2}\nabla u\big)=f(x,u),\quad w\in \mathcal{A}_p,\] on smooth domain and for varying nonlinea
Externí odkaz:
https://doaj.org/article/d9ab7a051f3644e1a0511ff54391d464
Autor:
Kaushik Bal, Prashanta Garain
Publikováno v:
Electronic Journal of Differential Equations, Vol 2019, Iss 95,, Pp 1-12 (2019)
In this article we present some nonexistence results concerning stable solutions to the equation $$ \hbox{div}\big(w(x)|\nabla u|^{p-2}\nabla u\big) =g(x)f(u)\quad \text{in }\mathbb{R}^N,\;p\geq 2 $$ when f(u) is either $u^{-\delta}+u^{-\gamma}
Externí odkaz:
https://doaj.org/article/8ff8b83185d24fd8b638c5921e61b733
Autor:
Prashanta Garain, Juha Kinnunen
This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. It is based on energy estimates and the Moser iteration technique. Inst
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b6243189f3a822ef3fca01b91f94a92
https://aaltodoc.aalto.fi/handle/123456789/120537
https://aaltodoc.aalto.fi/handle/123456789/120537
Autor:
Prashanta Garain
In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish existence of at least one weak solution for a parameter dependent singular nonlinearity and existenc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::34153b4199f4975d1fda30445be87841
http://arxiv.org/abs/2301.02023
http://arxiv.org/abs/2301.02023
Autor:
Prashanta Garain, Juha Kinnunen
Publikováno v:
Proceedings of the American Mathematical Society. 149:3407-3416
In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincar\'e inequality. Our method is purely variational and to the be
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0fa3294c70a78e5aacb9503ee74321c0
https://doi.org/10.1090/proc/15417
https://doi.org/10.1090/proc/15417
Publikováno v:
Mathematische Zeitschrift. 299:1875-1895
This paper is concerned with the qualitative analysis of solutions to the following class of quasilinear problems $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{\Phi }u=f(x,u) &{}\quad \text {in } \Omega ,\\ u=0 &{}\quad \text {on }\partial \O
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9bb8af31a5ade57ffec23f8d5621ffa3
https://doi.org/10.1007/s00209-021-02757-z
https://doi.org/10.1007/s00209-021-02757-z
Autor:
Prashanta Garain, Kaushik Bal
Publikováno v:
manuscripta mathematica. 168:101-117
For a bounded smooth domain $$\Omega \subset {\mathbb {R}}^N$$ with $$N\ge 2$$ , we establish a weighted and an anisotropic version of Sobolev inequality related to the embedding $$W_{0}^{1,p}(\Omega )\hookrightarrow L^q(\Omega )$$ for $$1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::da4bc2736c0e5257280d8f4775755e70
https://doi.org/10.1007/s00229-021-01298-3
https://doi.org/10.1007/s00229-021-01298-3
Autor:
Prashanta Garain, Alexander Ukhlov
Publikováno v:
Analysis and Mathematical Physics. 12
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2739238bd17ad29b436b9997a07bb7a0
https://doi.org/10.1007/s13324-022-00676-8
https://doi.org/10.1007/s13324-022-00676-8
Autor:
Prashanta Garain
Publikováno v:
Complex Variables and Elliptic Equations. 66:2055-2075
Let $p_i\geq 2$ and consider the following anisotropic $p$-Laplace equation $$ -\sum_{i=1}^{N}\frac{\partial}{\partial x_i}\Big(\Big|\frac{\partial u}{\partial x_i}\Big|^{p_i-2}\frac{\partial u}{\partial x_i}\Big)=g(x)f(u),\,\,u>0\text{ in }\Omega. $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0dfe7dd5b00da52a0fedf754fb15059c
https://doi.org/10.1080/17476933.2020.1801655
https://doi.org/10.1080/17476933.2020.1801655