相关论文: Quantitative regularity for parabolic De Giorgi cl…

This paper is concerned with a class of quasilinear elliptic equations involving some potentials related to the Caffarelli-Korn-Nirenberg inequality. We prove the local boundedness and H\"older continuity of weak solutions by using the…

We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boundary of this class of domains is a mixed Lipschitz…

We obtain some "universal" estimates for $L_2$-norm of the solution of a parabolic equation via a weighted version of $H^{-1}$-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation…

In the elliptic theory for $p$-Laplacian-like problems, the H\"{o}lder continuity of solutions has been proven for problems arising as Euler--Lagrange equations of a convex potential with $p$-growth that additionally satisfies the splitting…

We establish the local H\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad 1<p<2,\quad 0<p-1<q. \] The proof…

We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised by Manfredi & Mingione…

This paper is concerned with H\"older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain,…

We study elliptic and parabolic systems in divergence form with degenerate or singular coefficients. Under the conormal boundary condition on the flat boundary, we establish boundary Schauder type estimates when the coefficients have…

We establish H\"older estimates for the time derivative of solutions of fully non-linear parabolic equations that does not necessarily have $C^{2,\alpha}$ estimates.

This paper is devoted to investigating the interior $C^{1, \alpha}$ regularity of viscosity solutions to the nonlocal double phase equations $$ \int_{\mathbb{R}^d}…

We study the local H\"{o}lder regularity of weak solutions to the fully fractional parabolic equations involving spatial fractional diffusion and fractional time derivatives of the Marchaud type. It is worth noting that we do not impose…

Under general conditions we show that the solution of a stochastic parabolic partial differential equation of the form \[ \partial_t u = \mathrm{div} (A \nabla u) + f(t,x, u) + g_i (t,x,u) \dot{w}^i_t \] is almost surely H\"older continuous…

We study elliptic and parabolic problems governed by the singular elliptic operators \begin{align*} \mathcal L=y^{\alpha_1}\mbox{Tr }\left(QD^2_xu\right)+2y^{\frac{\alpha_1+\alpha_2}{2}}q\cdot \nabla_xD_y+\gamma y^{\alpha_2}…

The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms of caloric Riesz potentials of the data. As a consequence of…

We study partial regularity for nondegenerate parabolic systems of double phase type, where the growth function is given by $H(z,s)=s^p+a(z)s^q$, $z=(x,t)\in\Omega_T$, with $\tfrac{2n}{n+2}<p\le q$ and $a(z)$ a nonnegative…

We prove the natural weighted Calder\'{o}n and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irregular obstacles. We also obtain Morrey regularity…

We consider the Dirichlet problem for a class of elliptic and parabolic equations in the upper-half space $\mathbb{R}^d_+$, where the coefficients are the product of $x_d^\alpha, \alpha \in (-\infty, 1),$ and a bounded uniformly elliptic…

The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to H\"{o}rmander's vector fields, where the coefficients are bounded with vanishing mean oscillation. We…

We study existence and regularity properties of solutions to the singular $p$-Laplacean parabolic system in a bounded domain $\Omega$. The main purpose is to prove global $L^r(\varepsilon,T;L^q(\Omega))$, $\varepsilon\geq0$, integrability…

We investigate a class of parametric elliptic eigenvalue problems with homogeneous essential boundary conditions where the coefficients (and hence the solution $u$) may depend on a parameter $y$. For the efficient approximate evaluation of…