Zobrazeno 1 - 10
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pro vyhledávání: '"Adimurthi"'
We establish Trudinger-type inequality in the context of fractional boundary Hardy-type inequality for the case $sp=d$, where $p>1, ~ s \in (0,1)$ on a bounded Lipschitz domain $\Omega \subset \mathbb{R}^d$. In particular, we establish fractional ver
Externí odkaz:
http://arxiv.org/abs/2410.19362
We prove fractional boundary Hardy's inequality in dimension one for the critical case $sp =1$. Optimality of the inequality is obtained for any $p$. The extra logarithmic correction term appears in usual fashion. We also provide a concrete (workable
Externí odkaz:
http://arxiv.org/abs/2407.12098
We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where optimal l
Externí odkaz:
http://arxiv.org/abs/2407.10863
Classical boundary Hardy inequality, that goes back to 1988, states that if $1 < p < \infty, \ ~\Omega$ is bounded Lipschitz domain, then for all $u \in C^{\infty}_{c}(\Omega)$, $$\int_{\Omega} \frac{|u(x)|^{p}}{\delta^{p}_{\Omega}(x)} dx \leq C\int_
Externí odkaz:
http://arxiv.org/abs/2405.09823
Autor:
Adimurthi, Karthik
In this paper, we show that weak solutions of $$-\text{div} \mathbb{A}(x)\nabla u = 0 \qquad \text{where}\quad \mathbb{A}(x)= \mathbb{A}(x)^T \,\, \text{and} \,\, \lambda |\zeta|^2 \leq \langle \mathbb{A}(x)\zeta,\zeta\rangle \leq \Lambda |\zeta|^2,$
Externí odkaz:
http://arxiv.org/abs/2405.03802
Publikováno v:
Advanced Nonlinear Studies, Vol 17, Iss 2, Pp 311-317 (2017)
We study existence and summability of solutions for elliptic problems with a power-like lower order term and a Hardy potential.We prove that, due to the presence of the lower order term, solutions exist and are more summable under weaker assumptions
Externí odkaz:
https://doaj.org/article/e790e8d38a40443280af6cfc4d60bf3c
We establish generalised fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of $s$ and $p$ on various domains in $\mathbb{R}^d, d \geq 1$. In particular, for Lipschitz bounded domains
Externí odkaz:
http://arxiv.org/abs/2308.11956
Autor:
Adimurthi, Karthik, Kim, Wontae
In this paper, we study some regularity issues concerning the gradient of weak solutions of $u_t - {\rm div} \mathcal{A}(x,t,\nabla u) = g$, where $\mathcal{A}(x,t,\nabla u)$ is modeled after the $p$-Laplace operator. The main results we are interest
Externí odkaz:
http://arxiv.org/abs/2307.02420
In this paper, we prove local H\"older continuity for the spatial gradient of weak solutions to $$u_t - \text{div} (|\nabla u|^{p-2}\nabla u) + \text{P.V.} \int_{\mathbb{R}^n} \frac{|u(x,t) - u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+ps}} \ dy = 0.$$ It
Externí odkaz:
http://arxiv.org/abs/2307.02363
Autor:
Adimurthi, Abhishek
In this note, we study the $L^1-$contractive property of the solutions the scalar conservation laws, got by the method of Lax-{O}le\u{\i}nik. First, it is proved when f is merely convex and the initial data is in $L^{\infty}(\mathbb{R})$. And then, i
Externí odkaz:
http://arxiv.org/abs/2306.17064