We prove the $$L_{p,q}$$ -solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces lowest integrability conditions. In particular, for are not necessarily bounded. study both Dirichlet conormal derivative boundary value problems on irregular domains. also embedding results Sobolev spaces, proof ...

Many of the most common and useful properties of Sobolev spaces defined over a domain (open set) in Euclidean space require that the domain has a minimal degree of regularity. To this end, the domain is often assumed to satisfy a “cone condition.” For example, various imbeddings of Sobolev spaces into Lebesgue spaces or spaces of bounded continuous functions (the Sobolev imbedding theorem), and...

Abstract We prove that if $$1&lt;p&lt;\infty $$ 1 &lt; p ∞ and $$\delta :]0,p-1]\rightarrow ]0,\infty [$$ δ : ] 0 , - →</mml:m...

We establish two inequalities of Stein-Weiss type for the Riesz potential operator Iα,γ (B−Riesz potential operator) generated by the Laplace-Bessel differential operator ΔB in the weighted Lebesgue spaces Lp,|x|β ,γ . We obtain necessary and sufficient conditions on the parameters for the boundedness of Iα,γ from the spaces Lp,|x|β ,γ to Lq,|x|−λ ,γ , and from the spaces L1,|x|β ,γ to the weak...

The structure of non-compactness optimal Sobolev embeddings m-th order into the class Lebesgue spaces and that all rearrangement-invariant function is quantitatively studied. Sharp two-sided estimates Bernstein numbers such are obtained. It shown that, whereas embedding within finitely strictly singular, in not even singular.

The properties of the metric topology on infinite and finite sets are analyzed. We answer whether finite metric spaces hold interest in algebraic topology, and how this result is generalized to pseudometric spaces through the Kolmogorov quotient. Embedding into Lebesgue spaces is analyzed, with special attention for Hilbert spaces, `p, and EN .

Abstract In this short paper, I recall the history of dealing with lack compactness a sequence in case an unbounded domain and prove vanishing Lions-type result for Lebesgue-measurable functions. This lemma generalizes some results class Orlicz–Sobolev spaces. What matters here is behavior integral, not space.

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.