27 citations · 117 across the 40 of their papers we have counts for
40 papers
The equivalence of solutions to fractional and logarithmic Helmholtz equations
A. Biswas, J. Groszkiewicz, P. R. Stinga
We show the following equivalence of solutions to general fractional Helmholtz equations: is a solution to for \textit{some} fixed and some if and o…
Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria
Pablo Seleson, Pablo Raúl Stinga, Mary Vaughan
This paper rigorously analyzes bond failure in the peridynamic theory of solid mechanics, which is a fundamental component of fracture modeling. We compare analytically and numeric…
Regularity of solutions to degenerate and singular free boundary problems with volume constraint
T. M. Nascimento, X. H. Nguyen, P. R. Stinga
We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.
Interior Schauder estimates for fractional elliptic equations in nondivergence form
P. R. Stinga, M. Vaughan
We obtain sharp interior Schauder estimates for solutions to nonlocal Poisson problems driven by fractional powers of nondivergence form elliptic operators $(-a^{ij}(x) \partial_{i…
Sharp extension problem characterizations for higher fractional power operators in Banach spaces
A. Biswas, P. R. Stinga
We prove sharp characterizations of higher order fractional powers , where is noninteger, ofgenerators of uniformly bounded -semigroups on Banach spaces via…
A PDE approach to the existence and regularity of surfaces of minimum mean curvature variation
L. A. Caffarelli, P. R. Stinga, H. Vivas
We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem $$\min_{\mathcal{M}}\frac{1}{2}\int_{\mathca…