Related papers: Potential estimates for the p-Laplace system with …
We establish local Calder\'on-Zygmund type estimates for weak solutions to nonlinear parabolic systems with $p$-growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to $L^{\mu s}$, where the…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we…
We investigate qualitative properties of weak solutions of the Dirichlet problem for the equation $-\Delta_p u = \lambda m(x)|u|^{p-2}u + \eta a(x)|u|^{q-2}u + f(x)$ in a bounded domain $\Omega \subset \mathbb{R}^N$, where $q<p$. Under…
We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have H\"older continuous gradients, and prove versions of the generalized maximum principle, the $C^{1,\alpha}$-estimate,…
We establish a class of pointwise estimates for weak solutions to mixed local and nonlocal parabolic equations involving measure data and merely measurable coefficients via caloric Riesz potentials. Such estimates effectively bound the…
We prove in this paper the global Lorentz estimate in term of fractional-maximal function for gradient of weak solutions to a class of p-Laplace elliptic equations containing a non-negative Schr\"odinger potential which belongs to reverse…
The minimax risk is often considered as a gold standard against which we can compare specific statistical procedures. Nevertheless, as has been observed recently in robust and heavy-tailed estimation problems, the inherent reduction of the…
We study existence and regularity of weak solutions for the following $p$-Laplacian system \begin{cases} -\Delta_p u+A\varphi^{\theta+1}|u|^{r-2}u=f, \ &u\in W_0^{1,p}(\Omega),\\-\Delta_p \varphi=|u|^r\varphi^\theta, \ &\varphi\in…
We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a…
The pointwise gradient estimate for weak solution pairs to the stationary Stokes system with Dini-BMO coefficients is established via the Havin-Maz'ya-Wolff type nonlinear potential of the nonhomogeneous term. In addition, we present a…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
In this paper, we investigate the existence of solutions for a class of $p$-Laplacian fractional order Kirchhoff-type system with Riemann-Liouville fractional derivatives and a parameter $\lambda$. By mountain pass theorem, we obtain that…
In this article we investigate the temporal regularity of strong solutions to the stochastic $p$-\com{L}aplace system in the degenerate setting, $p \in [2,\infty)$, driven by a multiplicative nonlinear stochastic forcing. We establish $1/2$…
In this paper we obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard $p(x)-$type growth. A model equation is the inhomogeneous $p(x)-$laplacian. Namely, \[…
In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler--Lagrange equations. We show that weak solutions are locally bounded…
This article concerns with the global H\"older regularity of weak solutions to a class of problems involving the fractional $(p,q)$-Laplacian, denoted by $(-\Delta)^{s_1}_{p}+(-\Delta)^{s_2}_{q}$, for $1<p,q<\infty$ and $s_1,s_2\in (0,1)$.…
Let $n \in \{2, 3, 4, \ldots\}$, $N \in \{1, 2, 3, \ldots\}$ and $p \in \big(1, 2-\frac{1}{n}\big]$. Let $\beta \in (1,\infty)$ be such that \[ \frac{np}{n-p}<\beta'<\frac{n}{n(2-p)-1} \] and $f \in L^{\beta}(\mathbb R^n;\mathbb R^N)$.…
We deal with the existence of weak solutions for a mixed Neumann-Robin-Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We…