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pro vyhledávání: '"35D30"'
In this paper, we consider Dirichlet boundary value problem involving the anisotropic $p(x)$-Laplacian, where $p(x)= (p_1(x), ..., p_n(x))$, with $p_i(x)> 1$ in $\overline{\Omega}$. Using the topological degree constructed by Berkovits, we prove, und
Externí odkaz:
http://arxiv.org/abs/2411.03123
Autor:
Ochoa, Pablo, Silva, Analía
In this paper, we introduce a new higher-order Laplacian operator in the framework of Orlicz-Sobolev spaces, the biharmonic g-Laplacian $$\Delta_g^2 u:=\Delta \left(\dfrac{g(|\Delta u|)}{|\Delta u|} \Delta u\right),$$ where $g=G'$, with $G$ an N-func
Externí odkaz:
http://arxiv.org/abs/2411.01276
We discuss a nonlinear system of partial differential equations modelling the formation of granuloma during tuberculosis infections and prove the global solvability of the homogeneous Neumann problem for \begin{align*} \begin{cases} u_t = D_u \Delta
Externí odkaz:
http://arxiv.org/abs/2411.00542
Autor:
Ahmed, Irshaad, Fiorenza, Alberto, Formica, Maria Rosaria, Gogatishvili, Amiran, Hamidi, Abdallah El
We present some regularity results on the gradient of the weak or entropic-renormalized solution $u$ to the homogeneous Dirichlet problem for the quasilinear equations of the form \begin{equation*}\label{p-laplacian_eq} -{\rm div~}(|\nabla u|^{p-2}\n
Externí odkaz:
http://arxiv.org/abs/2411.00367
We propose some general growth conditions on the function $% f=f\left( x,\xi \right) $, including the so-called natural growth, or polynomial, or $p,q-$growth conditions, or even exponential growth, in order to obtain that any local minimizer of the
Externí odkaz:
http://arxiv.org/abs/2410.22875
We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for periodic initi
Externí odkaz:
http://arxiv.org/abs/2410.20493
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel inviscid, non
Externí odkaz:
http://arxiv.org/abs/2410.16743
Autor:
Cruz-Uribe, David
It is well known that non-negative solutions to the Dirichlet problem $\Delta u =f$ in a bounded domain $\Omega$, where $f\in L^q(\Omega)$, $q>\frac{n}2$, satisfy $\|u\|_{L^\infty(\Omega)} \leq C\|f\|_{L^q(\Omega)}$. We generalize this result by repl
Externí odkaz:
http://arxiv.org/abs/2410.17054
Autor:
Rutkowski, Artur
We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with respect to the space-time isotropic $\alpha$-stable process. We also prov
Externí odkaz:
http://arxiv.org/abs/2410.16188
Autor:
Elbar, Charles
We prove $L^{\infty}_{t}W^{1,p}_{x}$ Sobolev estimates in the Keller-Segel system by proving a functional inequality, inspired by the Brezis-Gallou\"et-Wainger inequality. These estimates are also valid at the discrete level in the Jordan-Kinderlehre
Externí odkaz:
http://arxiv.org/abs/2410.15095