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Regularity and singularities in elliptic PDE's: beyond monotonicity formulas

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Publications

Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials

Author(s): A. Enciso, A. Shao, B. Vergara
Published in: J. Eur. Math. Soc., 2020, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1105

New boundary Harnack inequalities with right hand side

Author(s): Xavier Ros-Oton, Damià Torres-Latorre
Published in: Journal of Differential Equations, 288, 2021, Page(s) 204-249, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2021.04.012

Generic regularity of free boundaries for the obstacle problem

Author(s): Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: Publications mathématiques de l'IHÉS, 2020, ISSN 0073-8301
Publisher: Springer Verlag
DOI: 10.1007/s10240-020-00119-9

A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems

Author(s): Audrito, Alessandro; Serra, Enrico; Tilli, Paolo
Published in: Comm. PDE, 2021, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1931884

Sharp quantitative stability for isoperimetric inequalities with homogeneous weights

Author(s): Cinti, Eleonora; Glaudo, Federico; Pratelli, Aldo; Ros-Oton, Xavier; Serra, Joaquim
Published in: Trans. AMS, 2022, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8525

Stable solutions to semilinear elliptic equations are smooth up to dimension $9$

Author(s): Xavier Cabré, Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: Acta Mathematica, 224/2, 2020, Page(s) 187-252, ISSN 0001-5962
Publisher: Royal Swedish Academy of Sciences
DOI: 10.4310/acta.2020.v224.n2.a1

Obstacle problems for integro-differential operators: Higher regularity of free boundaries

Author(s): Nicola Abatangelo, Xavier Ros-Oton
Published in: Advances in Mathematics, 360, 2020, Page(s) 106931, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2019.106931

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Author(s): Fernández-Real, Xavier; Ros-Oton, Xavier
Published in: Arch. Rat. Mech. Anal., 240, 2021, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-021-01617-8

Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation

Author(s): A. Ruland, M. A. Garcia-Ferrero, W. Zaton
Published in: Inverse problems and imaging, 2022, ISSN 1930-8337
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2021049

The Neumann problem for the fractional Laplacian: regularity up to the boundary

Author(s): Audrito, Alessandro; Felipe-Navarro, Juan-Carlos; Ros-Oton, Xavier
Published in: Ann. Sc. Norm. Super. Pisa Cl. Sci., 2022, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.202105_096

The Dirichlet problem for nonlocal elliptic operators with $C^{0,\alpha }$ exterior data

Author(s): Alessandro Audrito, Xavier Ros-Oton
Published in: Proceedings of the American Mathematical Society, 148/10, 2020, Page(s) 4455-4470, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/15121

The fractional obstacle problem with drift: Higher regularity of free boundaries

Author(s): Teo Kukuljan
Published in: Journal of Functional Analysis, 281/8, 2021, Page(s) 109114, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109114

Higher order parabolic boundary Harnack inequality in $C^1$ and $C^{k,\alpha}$ domains

Author(s): Kukuljan, Teo
Published in: Disc. Cont. Dyn. Syst., 2022, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2021207