Zobrazeno 1 - 10
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pro vyhledávání: '"35b45"'
Autor:
Dong, Hongjie, Kwon, Hyunwoo
We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder estimates for
Externí odkaz:
http://arxiv.org/abs/2412.20125
Autor:
Castro, Hernán
In this article we study the quasi-linear equation \[ \left\{ \begin{aligned} \mathrm{div}\, \mathcal A(x,u,\nabla u)&=\mathcal B(x,u,\nabla u)&&\text{in }\Omega,\\ u\in H^{1,p}_{loc}&(\Omega;wdx) \end{aligned} \right. \] where $\mathcal A$ and $\mat
Externí odkaz:
http://arxiv.org/abs/2412.07866
In this paper, we study three kinds of nonlinear degenerate elliptic equations containing the Grushin operator. First, we prove radial symmetry and a decay rate at infinity of solutions to such a Grushin equation by using the moving plane method in c
Externí odkaz:
http://arxiv.org/abs/2412.08039
Autor:
Quittner, Pavol
We consider a priori estimates of possibly sign-changing solutions to superlinear parabolic problems and their applications (blow-up rates, energy blow-up, continuity of blow-up time, existence of nontrivial steady states etc). Our estimates are base
Externí odkaz:
http://arxiv.org/abs/2412.05855
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a quasi-best a
Externí odkaz:
http://arxiv.org/abs/2412.05965
Autor:
Sauer, Jonas, Smith, Scott A.
In this expository note, we show that the blow-up arguments of L. Simon adapt well to the corresponding Schauder theory of germs used in the study of singular SPDEs. We illustrate this through some representative examples. As in the classical PDE fra
Externí odkaz:
http://arxiv.org/abs/2412.01486
Autor:
Cheikh-Ali, Hussein, Premoselli, Bruno
Let $\Omega$ be a bounded, smooth connected open domain in $\mathbb{R}^n$ with $n\geq 3$. We investigate in this paper compactness properties for the set of sign-changing solutions $v \in H^1_0(\Omega)$ of \begin{equation} \tag{*} -\Delta v+h v =\lef
Externí odkaz:
http://arxiv.org/abs/2412.00817
Autor:
Xu, Ziyi
We investigate the $W^{1,p}$ estimates of the Neumann problem for the Schr\"odinger equation $-\Delta u+ V u={\rm div}(f)$ in the region above a convex graph. For any $p>2$, we obtain a sufficient condition for the $W^{1,p}$ solvability. As a result,
Externí odkaz:
http://arxiv.org/abs/2411.18852
In this paper we investigate the $L^p$ regularity, $L^p$ Neumann and $W^{1,p}$ problems for generalized Schr\"odinger operator $-\text{div}(A\nabla )+ V $ in the region above a Lipschitz graph under the assumption that $A$ is elliptic, symmetric and
Externí odkaz:
http://arxiv.org/abs/2411.18458
Autor:
Esquivel, Salvador, Weber, Hendrik
We show a priori bounds for the dynamic fractional $\Phi^4$ model on $\mathbb{T}^3$ in the full subcritical regime using the framework of Hairer's regularity structures theory. Assuming the model bounds our estimates imply global existence of solutio
Externí odkaz:
http://arxiv.org/abs/2411.16536