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We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.

Fundamental inequalities on firmly stratified sets and some applications.

Nicaise, Serge, Penkin, Oleg M. (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials

Kazuhiro Kurata, Satoko Sugano (2000)

Studia Mathematica

We show a weighted version of Fefferman-Phong's inequality and apply it to give an estimate of fundamental solutions, eigenvalue asymptotics and exponential decay of eigenfunctions for certain degenerate elliptic operators of second order with positive potentials.

Fundamental Solutions and Eigenfunction Expansions for Schrödinger Operators . I. Fundamental Solutions.

Hitoshi Kitada (1988)

Mathematische Zeitschrift

Fundamental Solutions and Eigenfunction Expansions for Schrödinger Operators. II. Eigenfunction Expansions.

Arne Jensen, Hitoshi Kitada (1988)

Mathematische Zeitschrift

Funktionenfamilien mit einem Maximumprinzip und elliptische Differentialgleichungen II.

St. Ruscheweyh, Gerhard Jank (1975)

Monatshefte für Mathematik

Funktionenfamilien mit einem Maximumprinzip und elliptische Differentialgleichungen I.

Stephan Ruscheweyh (1974)

Monatshefte für Mathematik

Further qualitative properties for elliptic equations in unbounded domains

Henri Berestycki, Luis Caffarelli, Louis Nirenberg (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Further remark on a theorem by E. M. Landesman and A. C. Lazer

Svatopluk Fučík (1974)

Commentationes Mathematicae Universitatis Carolinae

Gagliardo-Nirenberg inequalities in logarithmic spaces

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2006)

Colloquium Mathematicae

We obtain interpolation inequalities for derivatives: $\int M_{q, α} (| \nabla f (x) |) d x \leq C [\int M_{p, β} (Φ ₁ (x, | f |, | \nabla^{(2)} f |)) d x + \int M_{r, γ} (Φ ₂ (x, | f |, | \nabla^{(2)} f |)) d x]$ , and their counterparts expressed in Orlicz norms: ||∇f||²(q,α) ≤ C||Φ₁(x,|f|,|∇(2)f|)||(p,β) ||Φ₂(x,|f|,|∇(2)f|)||(r,γ) $,$ where ${| | \cdot | |}_{(s, κ)}$ is the Orlicz norm relative to the function $M_{s, κ} (t) = t^{s} {(l n (2 + t))}^{κ}$ . The parameters p,q,r,α,β,γ and the Carathéodory functions Φ₁,Φ₂ are supposed to satisfy certain consistency conditions. Some of the classical Gagliardo-Nirenberg inequalities follow as a special case. Gagliardo-Nirenberg inequalities in logarithmic spaces with higher...

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Function theory for a Beltrami algebra.

Functional determinants and geometry .

Functional determinants and geometry (Erratum).

Functionals with linear growth in the calculus of variations. I.

Functionals with linear growth in the calculus of variations. II.

Functions of four variables which satisfy both the heat equation and the Laplace equation in three variables - II

Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains