Erik Lindgren

*Researcher *

**Adress:**
Lindstedtsvägen 25, 100 44 Stockholm

**Office:**
3646

**Phone:
**+46-7906643

**Email:**
eriklin (snabel-a) kth.se

**Mathematical
interest:** Free boundary problems, variational problems and PDE:s
in general.

** Meetings:
**Symposium in nonlinear PDEs, June 3-5 2013, Trondheim
, Norwegian-Italian Workshop in PDEs, December 2012

**Teaching:
**
Envariabelanalys SF1625 för CLGYM och CTKEM, HT16,
Differentialekvationer I SF1633, HT16,
Envariabelanalys SF1625 för öppen ingång, HT15,
Matematik baskurs, SF1659, HT15,
Analys för doktorander, VT15,
Envariabelanalys SF1625 för öppen ingång, HT14,
Matematik baskurs, SF1659, HT14,
TMA4122
4M, HT2012 , TMA4122
4M, HT2011

**Papers:**

A free boundary problem with constant Bernoulli-type boundary condition, joint work with Yannick Privat (Nancy), Nonlinear Analysis: Theory, Methods & Applications, Volume 67, Issue 8, 15 October 2007, Pages 2497-2505.

Regularity of the free boundary for a semilinear elliptic problem in two dimensions, joint work with Arshak Petrosyan (Purdue), published in Indiana Univ. Math J. 57 (2008), 3397-3418.

The N-membranes problem, joint work with Abdolrahman Razani (Imam Khomeini International University), published in Bulletin of the IMS, Volume 35, No. 1, April 2009..

The two-phase obstacle problem for the p-laplacian when p~2, joint work with Anders Edquist (KTH), published in Calc. Var. Partial Differential Equations 35 (2009), no. 4, 421–433..

On the two-phase membrane problem with coefficients below the Lipschitz threshold, joint work with Anders Edquist and Henrik Shahgholian (both at KTH), published in Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, 2359–2372.

On the penalized obstacle problem in the unit half ball, published in Electron. J. Differential Equations 2010, No. 09, 12 pp..

Regularity of a parabolic free boundary problem with Hölder continuous coefficients, joint work with Anders Edquist (KTH), published in Comm. Partial Differential Equations 37 (2012), no. 7, 1161–1185.

The Hölder infinite Laplacian and Hölder extensions, joint work with Antonin Chambolle (CMAP) and Régis Monneau (CERMICS), published in ESAIM Control Optim. Calc. Var. 18 (2012), no. 3, 799–835.

Optimal regularity of a parabolic free boundary problem of two-phase type with coefficients worse than Lipschitz, , joint work with Jyotshana V. Prajapat (Petroleum Institute), published, Potential Anal. 37 (2012), no. 2, 103–123.

Stability for the Infinity-Laplace Equation with variable exponent, arxiv preprint, joint work with Peter Lindqvist (NTNU), Differential and Integral Equations 25 (2012), no. 5-6, 589-600.

Optimal regularity for the no-sign obstacle problem, arxiv preprint, joint work with John Andersson (Warwick) and Henrik Shahgholian (KTH), Comm. Pure Appl. Math. 66 (2013), no. 2, 245–262.

On the regularity of solutions of the inhomogeneous infinity Laplace equation, arxiv preprint, Proc. Amer. Math. Soc. 142 (2014), no. 1, 277–288., .

Pointwise estimates for the heat equation. Application to the free boundary of the obstacle problem with Dini coefficients , arxiv preprint, Indiana Univ. Math. J. 62 (2013), no. 1, 171–199, joint work with Régis Monneau (CERMICS).

Tangential touch between the free and the fixed boundary in a semilinear free boundary problem in two dimensions , preprint, Ark. Mat. 52 (2014), no. 1, 21–42, joint work with Mahmoudreza Bazarganzadeh (Uppsala University).

Fractional eigenvalues, arxiv preprint, joint work with Peter Lindqvist (NTNU), Calc. Var. Partial Differential Equations 49 (2014), no. 1-2, 795–826.

Optimal Regularity for the parabolic No-Sign Obstacle Problem, arxiv preprint, joint work with John Andersson (Warwick) and Henrik Shahgholian (KTH), published in Interfaces Free Bound. 15 (2013), no. 4, 477–499.

The two-phase fractional obstacle problem, arxiv, SIAM J. Math. Anal. 47 (2015), no. 3, 1879–1905, joint work with Mark Allen and Arshak Petrosyan (both at Purdue University)

Pointwise regularity of the free boundary for the parabolic obstacle problem, arxiv, Calc. Var. Partial Differential Equations 54 (2015), no. 1, 299–347 (online version), joint work with Régis Monneau (CERMICS)

The fractional Cheeger problem, arxiv, Interfaces Free Bound. 16 (2014), 419-458, joint work with Lorenzo Brasco and Enea Parini (both at Aix-Marseille Université)

Regularity of the p-Poisson equation in the plane, arxiv, accepted for publication in Journal d'Analyse Matématique, joint work with Peter Lindqvist (NTNU)

Optimal regularity for the obstacle problem for the p-Laplacian, arxiv, J. Differential Equations 259 (2015), no. 6, 2167–2179 (online version), joint work with John Andersson och Henrik Shahgholian (both at KTH)

Inverse iteration for p-ground states, Proc. Amer. Math. Soc. 144 (2016), no. 5, 2121–2131, arxiv, joint work with Ryan Hynd (UPenn)

A doubly nonlinear evolution for the optimal Poincaré inequality, arxiv, Calc. Var. Partial Differential Equations 55 (2016), no. 4, 55:100, joint work with Ryan Hynd (UPenn)

Hölder estimates for viscosity solutions of equations of fractional p-Laplace type, arxiv, NoDEA Nonlinear Differential Equations Appl. 23 (2016), no. 5, 23:55

Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case, arxiv, Advances in Mathematics Volume 304, 2 January 2017, Pages 300–354, joint work with Lorenzo Brasco (Aix-Marseille Université)

Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution, accepted for publication in Analysis & PDE, arxiv, joint work with Ryan Hynd (UPenn)

Approximation of the least Rayleigh quotient for degree p homogeneous functionals, arxiv, joint work with Ryan Hynd (UPenn)

Perron's Method and Wiener's Theorem for a Nonlocal Equation, arxiv, accepted for publication in Potential Analysis, joint work with Peter Lindqvist (NTNU)

Equivalence of solutions to fractional p-Laplace type equations, arxiv, accepted for publication in Journal de Mathématiques Pures et Appliquées, joint work with Janne Korvenpää and Tuomo Kuusi (both Aalto University)

Extremal functions for Morrey's inequality in convex domains , arxiv, joint work with Ryan Hynd (UPenn)

The $\infty$-harmonic potential is not always an $\infty$-eigenfunction, arxiv.