Zobrazeno 1 - 10
of 4 365
pro vyhledávání: '"35K55"'
Autor:
Dolbeault, Jean
Obtaining explicit stability estimates in classical functional inequalities like the Sobolev inequality has been an essentially open question for 30 years, after the celebrated but non-constructive result of G. Bianchi and H. Egnell in 1991. Recently
Externí odkaz:
http://arxiv.org/abs/2411.13271
We consider the optimal control of occupied processes which record all positions of the state process. Dynamic programming yields nonlinear equations on the space of positive measures. We develop the viscosity theory for this infinite dimensional par
Externí odkaz:
http://arxiv.org/abs/2411.12080
Autor:
George, Mathew, Guan, Bo
Over many decades fully nonlinear PDEs, and the complex Monge-Amp\`ere equation in particular played a central role in the study of complex manifolds. Most previous works focused on problems that can be expressed through equations involving real $(1,
Externí odkaz:
http://arxiv.org/abs/2411.10946
In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates. Both nois
Externí odkaz:
http://arxiv.org/abs/2411.01847
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:
Elliott, Charles M., Sales, Thomas
We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under
Externí odkaz:
http://arxiv.org/abs/2410.24147
Autor:
Andreucci, Daniele, Tedeev, Anatoli F.
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, roughly speaking of the type of the exponential of a power of the distance from the origin. We assume here the
Externí odkaz:
http://arxiv.org/abs/2410.23075
We consider a scalar parabolic partial differential equation on the interval with nonlinear boundary conditions that are asymptotically linear. As the parameter crosses critical values (e.g. the Steklov eigenvalues), it is known that there are large
Externí odkaz:
http://arxiv.org/abs/2410.22146
We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles that eith
Externí odkaz:
http://arxiv.org/abs/2410.15855
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