J. LeCrone, Y. Shao, G. Simonett: The surface diffusion and the Willmore flow for uniformly regular hypersurfaces (22 page manuscript: Submitted for Publication) arXiv:1901.00208.
J. LeCrone, G. Simonett: On quasilinear parabolic equations and continuous maximal regularity (27 page manuscript: Submitted for Publication) arXiv:1808.01032.
I. Blank, J. LeCrone: Perturbed obstacle problems in Lipschitz domains: Linear stability and non-degeneracy in measure (9 page manuscript: To appear in Rocky Mountain Journal of Mathematics) arXiv:1808.05257.
B. Benson, I. Blank, J. LeCrone: Mean value theorems for Riemannian manifolds via the obstacle problem. The Journal of Geometric Analysis (2018). DOI: 10.1007/s12220-018-0093-4.
J. LeCrone, G. Simonett: On the flow of non-axisymmetric perturbations of cylinders via surface diffusion. Journal of Differential Equations 260(6) (2016), 5510-5531. DOI: 10.1016/j.jde.2015.12.008
J. LeCrone, J. Prüss, M. Wilke: On quasilinear parabolic evolution equations in weighted Lp–spaces II. Journal of Evolution Equations, 14(3) (2014), 509–533. DOI: 10.1007/s00028-014-0226-6.
J. LeCrone: Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow. Interfaces and Free Boundaries, 16(1) (2014), 41–64. DOI: 10.4171/IFB/313.
J. LeCrone, G. Simonett: On stability and well-posedness of the axisymmetric surface diffusion flow. SIAM Journal on Mathematical Analysis, 45(5) (2013), 2834–2869. DOI: 10.1137/120883505.
J. LeCrone: Elliptic operators and maximal regularity on periodic little-Holder spaces. Journal of Evolution Equations, 12 (2012), 295–325. DOI: 10.1007/s00028-011-0133-z.
J. LeCrone, G. Simonett: Continuous maximal regularity and analytic semigroups. Dynamical Systems and Differential Equations, DCDS Supplement 2011: Proceedings of the 8th AIMS International Conference (Dresden, Germany), 963–970. (Refereed Publication) arXiv:1110.5690
Ph.D., Vanderbilt University 2012
B.S., Pacific University 2005
Partial Differential Equations
Free Boundary Problems