Related papers: Some Uniforme Estimates for Scalar Curvature Type …
We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the independent variables.
In this short note, we use classic computations for K\"ahler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.
In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.
We consider the problem $F=f(\nu)$ for strictly convex, closed hypersurfaces in hyperbolic space and solve it for curvature functions $F$ the inverses of which are of class $(K^*)$.
The paper develops various estimates for solutions of a fourth order nonlinear PDE, which corresponds to prescribing the scalar curvature of a toric Kahler metric.
Local Schauder estimates hold in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic variational problems and elliptic equations are locally H\"older continuous, provided coefficients are…
A new method to compute Schauder Estimates for multidimensional fourth order heat-type equations is proposed. In particular, we show how knowing Schauder or Sobolev estimates for the one-dimensional fourth order heat equation allows to…
We obtain some new inequalities of Chebyshev Type.
We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a…
We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form $f_t + v \cdot \nabla_x f = \mathcal L_v f + c$, where $\mathcal L_v$ is an integro-differential diffusion…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
We introduce a method of mixed convex integration and demonstrate its suitability for solving a particular class of semilinear second-order partial differential relations. As an application, we provide a new proof of a result on scalar…
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
We show sharp square function estimates for curves in the plane whose curvature degenerates at a point and estimates sharp up to endpoints for cones over these curves. To this end, for curves of finite type we extend the classical…
Let $f:S\to B$ be a finite cyclic covering fibration of a fibered surface. We study the lower bound of slope $\lambda_{f}$ when the relative irregularity $q_{f}$ is positive.
In this paper, we prove some new inequalities of Simpson's type for functions whose derivatives of absolute values are h-convex and h-concave functions. Some new estimations are obtained. Also we give some sophisticated results for some…
We establish two comparison results between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can…
Some forms of qKdV type equations are indicated which arise from Virasoro considerations.
We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.