Research

Supported by

National Science Foundation - Division of Mathematical Sciences Grant: "Higher-Order Nonlocal Models in Continuum Mechanics Award (2017-present)

Publications

• M. Foss, W. J. Hrusa & V. J. Mizel, The Lavrentiev Gap Phenomenon in Nonlinear Elasticity, Arch. Rational Mech. Anal. 167 (2003), 337-365.
• M. Foss, Global Regularity for Almost Minimizers of Nonconvex Variational Problems, Ann. Mat. Pura Appl. (4) 187 No. 2 (2008), 263-321.
• M. Foss & G. Mingione, Partial Continuity for Elliptic Problems, Ann. Inst. H. Poincare Anal. Non Lineaire, 25 No. 3 (2008), 471-503.
• V. Bogelein, M. Foss & G. Mingione, Regularity in Parabolic Systems with Continuous Coefficients, Math. Zeitschrift 270 No. 3-4 (2012), 903-938.
• M. Foss & C. S. Goodrich, On Partial Holder Continuity and a Caccioppoli Inequality for Aymptotically Convex Functionals between Riemannian Manifolds, Ann. Mat. Pura Appl. 195 No. 5 (2016), 1405-1461.
• M. Foss & P. Radu, Bridging local and nonlocal models: convergence and regularity, Handbook of Nonlocal Continuum Mechanics for Materials and Structures, edited by George Z. Voyiadjis, Springer 2018, 1-17.

Teaching

Undergraduate

• Calculus I and II
• Differential Equations
• Elementary Analysis
• Introduction to Partial Differential Equations
• Linear Algebra
• Mathematics for High School Teachers I

Graduate

• Advanced Methods in Applied Mathematics I and II
• Nonlinear Partial Differential Equations
• Partial Differential Equations
• Real Analysis I and II

Awards

College Distinguished Teaching Award - 2009

Certficate of Recognition for Contributions to Students from the UNL Parent's Association - 2007, 2009

Specializations

• Calculus of Variations
• Nonlocal Variation Problems
• Partial Differential Equations
• Integral Equations
• Continuum Mechanics
• Control of Mechanical System