2 citations · 3 across the 7 of their papers we have counts for
9 papers
Global Calderon-Zygmund estimates for irregular double-phase evolution problem with non-divergence data
Rakesh Arora, Sergey Shmarev
We study irregular double-phase parabolic equations with variable exponents and non-divergence data, \[ u_t-\operatorname{div} \left(\mathcal{F}(z,\nabla u)\nabla u \right)=f(z),\q…
Irregular double-phase evolution problem: existence and global regularity
Rakesh Arora, Sergey Shmarev
We investigate the homogeneous Dirichlet problem for the irregular double-phase evolution equation \[ u_t-\operatorname{div} \left( a(z)|\nabla u|^{p(z)-2} \nabla u + b(z)|\nabla u…
Global gradient estimates for solutions of parabolic equations with nonstandard growth
Rakesh Arora, Sergey Shmarev
We study how the smoothness of the initial datum and the free term affect the global regularity properties of solutions to the Dirichlet problem for the class of parabolic equation…
Optimal global second-order regularity and improved integrability for parabolic equations with variable growth
Rakesh Arora, Sergey Shmarev
We consider the homogeneous Dirichlet problem for the parabolic equation \[ u_t- \operatorname{div} \left(|\nabla u|^{p(x,t)-2} \nabla u\right)= f(x,t) + F(x,t, u, \nabla u) \] in…
Existence and global second-order regularity for anisotropic parabolic equations with variable growth
Rakesh Arora, Sergey Shmarev
We consider the homogeneous Dirichlet problem for the anisotropic parabolic equation \[ u_t-\sum_{i=1}^ND_{x_i}\left(|D_{x_i}u|^{p_i(x,t)-2}D_{x_i}u\right)=f(x,t) \] in the cylinde…
Existence and regularity results for a class of parabolic problems with double phase flux of variable growth
Rakesh Arora, Sergey Shmarev
We study the homogeneous Dirichlet problem for the equation \[ u_t-\operatorname{div}\left((a(z)\vert \nabla u\vert ^{p(z)-2}+b(z)\vert \nabla u\vert ^{q(z)-2})\nabla u\right)=f\qu…
Stability for evolution equations with variable growth
Sergey Shmarev, Jacson Simsen, Mariza Stefanello Simsen
We study the character of dependence on the data and the nonlinear structure of the equation for the solutions of the homogeneous Dirichlet problem for the evolution -Lapla…
Strong solutions of the double phase parabolic equations with variable growth
Rakesh Arora, Sergey Shmarev
This paper addresses the questions of existence and uniqueness of strong solutions to the homogeneous Dirichlet problem for the double phase equation with operators of variable gro…
Existence and nonuniqueness of segregated solutions to a class of cross-diffusion systems
Gonzalo Galiano, Sergey Shmarev, Julián Velasco
We study the the Dirichlet problem for the cross-diffusion system \[ \partial_tu_i=\operatorname{div}\left(a_iu_i\nabla (u_1+u_2)\right)+f_i(u_1,u_2),\quad i=1,2,\quad a_i=const>0,…