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Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers
Daniel E. Spector, Scott J. Spector
In this note two results are established for energy functionals that are given by the integral of over with $\nab…
BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension
Daniel E. Spector, Scott J. Spector
In this manuscript two estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the -seminorm of the gradient of a vect…
New Directions in Harmonic Analysis on
Daniel Spector
The study of what we now call Sobolev inequalities has been studied for almost a century in various forms, while it has been eighty years since Sobolev's seminal mathematical contr…
Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma
Daniel Spector, Jean Van Schaftingen
We prove a family of Sobolev inequalities of the form where $A (D) : C^\i…
Some remarks on boundary operators of Bessel extensions
Jesse Goodman, Daniel Spector
In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is \[Δ_x u(x,y) +\frac{1-2s}{y} \frac{\partial u}{\partial y}(x…
-theory for fractional gradient PDE with VMO coefficients
Armin Schikorra, Tien-Tsan Shieh, Daniel Spector
In this paper, we prove estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are . In particula…