Regularity theory in PDE plays an important role in the development of second-order elliptic and parabolic equations. Classical regularity estimates for elliptic and parabolic equations consist of Schauder estimates, L estimates, De Giorgi-Nash estimates, KrylovSafonov estimates, and so on. L and Schauder estimates, which play important roles in the theory of partial differential equations, are...

We prove that \(L_2(\mathbb {R})\) contains a Schauder basis of non-negative functions. Similarly, for all \(1<p<\infty \), \(L_{p}(\mathbb basic sequence functions such \(L_p(\mathbb embeds into the closed span sequence. as well if X is separable Banach space with bounded approximation property, then any set in dense quasi-basis (Schauder frame) X.

The paper is a comprehensive study of Lp and Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients on a half space and cylindrical domains with the conormal derivative boundary conditions. For the Lp estimates, we assume that the leading coefficients are only bounded and measurable in the t variable and have vanishing mean oscillations (VMOx) with...

We prove in this paper the existence of a Schauder basis for C[0, 1] consisting of rational functions of uniformly bounded degrees. This solves an open question of some years standing concerning the possible existence of such bases. This result follows from a more general construction of bases on R and [0, 1]. We prove that the new bases are unconditional bases for Lp , 1<p< , and Besov spaces....

We construct a Schauder basis for L1 consisting of non-negative functions and investigate unconditionally basic and quasibasic sequences of non-negative functions in Lp, 1 ≤ p < ∞.

*Correspondence: [email protected] 1Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain Full list of author information is available at the end of the article Abstract We prove a new fixed point theorem of Schauder type, which applies to discontinuous operators in noncompact domains. In order to do so, we...