I am an Assistant Professor at Brigham Young University. I do research in free boundary problems which involves analysis, partial differential equations, and the calculus of variations. I also research nonlocal parabolic differential equations where the time derivative is nonlocal.
Listed below are my papers.
M. Allen, D. Krivenstov, R. Neumayer, Quantitative Resolvent and Eigenfunction Stability for the Faber-Krahn Inequality, arxiv.org/abs/2504.13053
M. Allen, D. Kriventsov, H. Shahgholian, The free boundary for semilinear problems with highly oscillating singular terms, J. Lond. Math. Soc. (2) 111 (2025) no. 5, Paper No. e70180 arxiv.org/pdf/2405.10418
M. Allen, D. Kriventsov, R. Neumayer, Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit. Math. Ann. 391 (2025), no. 4, 6251-6289. https://arxiv.org/abs/2210.03552
M. Allen, M. Smit Vega Garcia, Two-phase almost minimizers for a fractional free boundary problem, NoDEA Nonlinear Differential Equations Appl. 31 (2024), Paper No 45. arxiv.org/abs/2308.06357
M. Allen, D. Kriventsov, R. Neumayer, Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula. Ars Inven. Anal. (2023), No. 1, 49pp. https://arxiv.org/abs/2107.03505
M. Allen, D. Kriventsov, R. Neumayer, Linear stability implies nonlinear stability for Faber-Krahn inequalities, Interfaces Free Bound. 25 (2023), no. 2, 217-324. https://arxiv.org/abs/2107.03495
M. Allen, B. Barker, J. Gardiner, and M. Zhao, Minimizers of a free boundary problem on three-dimensional cones, Nonlinear Anal. 226 (2023), Paper No. 113152. https://arxiv.org/abs/2101.02262
M. Allen, H. Shahgholian, and D. Kriventsov, The Inhomogeneous Boundary Harnack Principle for Fully Nonlinear and p-Laplace equations, Annales De l'IHP (C)-ANL 40 (2023), no. 1, 133-156. https://arxiv.org/pdf/2010.11854.pdf
M. Allen and M. Smit Vega Garcia, The fractional unstable obstacle problem, Nonlinear Anal. 193 (2020), 111459, 19pp. https://arxiv.org/pdf/1811.12497.pdf
M. Allen and D. Kriventsov, A spiral interface with positive Alt-Caffarelli-Friedman limit at the origin, Analysis & PDE Vol 13 (2020), No. 1, 201-214 https://arxiv.org/pdf/1801.01940.pdf
M. Allen and H. Shahgholian, A new boundary Harnack principle (equations with right hand side), Arch. Ration. Mech. Anal. 234 (2019) no. 3 1413-1444. https://arxiv.org/pdf/1811.12908.pdf
M. Allen, Uniqueness for weak solutions of parabolic equations with a fractional time derivative, New developments in the analysis of nonlocal operators, 137-148, Contemp. Math., 723. https://arxiv.org/pdf/1705.03959.pdf
M. Allen, A Fractional Free Boundary Problem related to a Plasma Problem, Communications in Analysis and Geometry ,Vol. 27, No. 8 (2019) pp. 1665-1696. http://arxiv.org/pdf/1507.06289.pdf
M. Allen, Holder regularity for nondivergence nonlocal parabolic equations, Calc. Var. Partial Differential Equations 57 (2018), no 4. https://arxiv.org/pdf/1610.10073.pdf
M. Allen, A Nondivergence Parabolic Problem with a Fractional Time Derivative. Differential Integral Equations 31 (2018), no. 3-4, 215-230.
M. Allen, A free boundary problem on three-dimensional cones. J. Differential Equations 263 (2017), no. 12, 8481–8507.
M. Allen, L. Caffarelli, A. Vasseur, Porous Medium Flow with both a Fractional Potential Pressure and Fractional Time Derivative. Chin. Ann. Math. Ser. B 38 (2017), no. 1, 45–82.
Mark Allen and Wenhui Shi, The Two-Phase Parabolic Signorini Problem, Indiana Univ. Math. J. 65 (2016), no. 2, 727-741.
M. Allen, L. Caffarelli, A. Vasseur, A Parabolic Problem with a Fractional Time Derivative. Arch. Ration. Mech. Anal. 221 (2016), no. 2, 603-630.
M. Allen, E. Lindgren and A. Petrosyan, The Two-Phase Fractional Obstacle Problem. SIAM J. Math. Anal. 47(2015), no. 3, 1879-1905.
Mark Allen and H. Chang Lara, Free Boundaries on two dimensional cones, J. Geom. Anal. 25 (2015), no. 3, 1547-1575).
Mark Allen, Separation of a lower-dimensional free boundary in a two phase problem, Math. Res. Lett 19 (2012), no.5, 1055-1074.
Mark Allen and Arshak Petrosyan, A two-phase problem with a lower-dimensional free boundary, Interfaces Free Bound. 14 (2012), no. 3, 307-342.
Talks given:
PDE seminar at ASU, Nov 2024
Applied math seminar at University of Utah, Oct 2024
2 talks at AMS sectional meeting, Albany NY, Oct 2024
Colloquium at New Mexico State, Sep 2024
International Conference on free boundary problems, Brazil, Aug 2024
Conference on Regularity theory and free boundary problems, Coimbra Portugal, July 2024
AMS sectional meeting, Tallahassee Florida, Mar 2024
PDE seminar at ASU, Nov 2023
PDE seminar at UNLV, Oct 2023
AMS Sectional meeting, Omaha NE, Oct 2023
Congress of Romanian Mathematicians, Jul 2023
AIMS conference in Wilmington NC, Jun 2023
Colloquium at University of Nebraska, Feb 2023
Continuum mechanincs seminar at University of Nebraska, Feb 2023
AWM special session at JMM in Boston, Jan 2023
Analysis Seminar at University of Sussex, Brighton England, Nov 2022
Colloquium at Linkoping University, Linkoping Sweden, Nov 2022
Mittag-Leffler Insitute, Stockholm Sweden, Sep 2022
Applied Math Seminar at University of Utah, Apr 2022
AMS Spring Sectional Meeting (virtual), Mar 2022
Geometry and Analysis seminar at Columbia University (virtual), Nov 2021
AMS Fall Central Sectional Meeting (virtual), Oct 2021
AIMS-Cameroon Research Center colloquium (virtual), Sep 2021
15th International Conference on Free Boundary Problems, Berlin (online), Sep 2021
Barrett Lectures at Univ Tennessee at Knoxville (online), May 2021
Rio de Janeiro Webinar on Analysis and PDEs, Sep 2020
Colloquium at Oregon State University, Feb 2020
Analysis seminar at Oregon State University, Feb 2020
12th Americas Conference on Differential Equations and Nonlinear Analysis, CIMAT Mexico, Dec 2019
AMS sectional meeting UC Riverside Nov 2019
Analysis Seminar at Northwestern University, Sep 2019
AMS sectional meeting Madison, Wisconsin, Sep 2019
Swedish Summer PDEs at KTH in Stockholm, Aug 2019
Analysis Seminar at Rutgers University, Feb 2019
Applied Math Seminar at Brigham Young University, Nov 2018
Applied Math Seminar at Utah State University, Oct 2018
AMS sectional meeting Ann Arbor, Michigan, Oct 2018
Nonlinear Phenomena Conference at George Washington University, Apr 2018
Mini-conference in PDEs at KTH in Stockholm, Dec 2017
Rainwater seminar at University of Washington, Oct 2017
14th International Conference on Free Boundary Problems, Shanghai China, July 2017
University of Utah, Applied Mathematics Seminar, Apr 2017
Colloquium Talk at Iowa State University, Mar 2017
University of Minnesota PDE Seminar, Feb 2017
University of Minnesota, Analysis and PDE working seminar, Feb 2017
AMS sectional meeting Minneapolis, MN, Oct 2016
Talk at 3rd Conference on Nonlocal Operators and PDE at Bedlewo Poland, June 2016
Talk at IBII/ICMA at Sam Houston State University, April 2016
SIAM conference on analysis of partial differential equations, Dec 2015
Colloquium Talk at Fordham University, Dec 2015
Colloquium Talk at Brigham Young University, Nov 2015
Invited Talk at 6th Symposium on Analysis and PDEs at Purdue University, May 2015
Analysis Seminar at Columbia University, Oct 2014
Seminar Talk at the University of Utah, July 2014
Colloquium Talk at Brigham Young University. Feb 2013
Contributed Talk at Joint Mathematical Meetings in San Diego, CA. Jan 2013
Contributed Talk at the Midwest PDE Seminar in Memphis, Tennessee. Nov 2012
Talk at Analysis Seminar at The University of Texas at Austin. Oct 2012
Contributed Talk at the 5th Symposium on Analysis and PDE's at Purdue University. May 2012
Talk at Analysis Seminar at The University of Texas at Austin. Feb 2012
Talk at PDE Seminar at Purdue University. Feb 2012