In this paper, we present a proof of Schauder estimate on Euclidean space and use it to generalize Donaldson’s with conical singularities in the following two directions. The first is that allow total cone angle be larger than 2 $$\pi $$ second discuss higher-order estimates.

We consider some reaction-diffusion equations perturbed by white noise and prove Schauder estimates for the elliptic problem associated with the generator of the corresponding transition semigroup, defined in the Banach space of continuous functions. This requires the proof of some new interpolation result. 2000 Mathematics Subject Classification AMS: 35R15, 60H15, 35B45

Existence results for semilinear systems of abstract evolution inclusions are established by means of Nadler, Bohnenblust-Karlin and Leray-Schauder fixed point theorems and a new technique for the treatment of systems based on vector-valued metrics and convergent to zero matrices.

We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.

In this article, we establish the existence results for boundary value problems of the singular fractional differential systems. Our analysis relies on the well known Leray-Schauder nonlinear alternative theory. An example is presented to illustrate the main results. 2000 Mathematics Subject Classification: 92D25, 34A37, 34K15.

The classical Schauder type results on C-regularity of solutions are exposed for linear second order elliptic equations with Hölder coefficients. Our approach is based on equivalent seminorms in Hölder spaces C, which are similar to seminorms introduced by S. Campanato [1]. Under this approach, the C-estimates for solutions are derived from the maximum principle and the interior smoothness of h...

In this paper, by using the Schauder fixed point theorem and the Banach contraction principle, we investigate existence and uniqueness of solutions for a class of multi-point boundary value problems of nonlinear fractional q-difference equations. As applications, two examples are presented to show the effectiveness of the obtained results.

Under suitable assumptions we prove, via the Leray-Schauder fixed point theorem, the existence of a solution for quasilinear elliptic boundary value problem in C(Ω̄) ∩ W (Ω), q > N which satisfies in addition the condition, (1+ | x |) 1 2u ∈ C(Ω̄).