Edelen, Nick; Spolaor, Luca; Velichkov, Bozhidar The symmetric (log-)epiperimetric inequality and a decay-growth estimate. (English) Zbl 07782493 Calc. Var. Partial Differ. Equ. 63, No. 1, Paper No. 2, 29 p. (2024). MSC: 35J20 35R35 PDFBibTeX XMLCite \textit{N. Edelen} et al., Calc. Var. Partial Differ. Equ. 63, No. 1, Paper No. 2, 29 p. (2024; Zbl 07782493) Full Text: DOI arXiv
Maiale, Francesco Paolo; Tortone, Giorgio; Velichkov, Bozhidar Epsilon-regularity for the solutions of a free boundary system. (English) Zbl 07755950 Rev. Mat. Iberoam. 39, No. 5, 1947-1972 (2023). MSC: 35R35 35B65 35D40 35J88 PDFBibTeX XMLCite \textit{F. P. Maiale} et al., Rev. Mat. Iberoam. 39, No. 5, 1947--1972 (2023; Zbl 07755950) Full Text: DOI arXiv
Mazzoleni, Dario; Trey, Baptiste; Velichkov, Bozhidar Regularity of the optimal sets for the second Dirichlet eigenvalue. (English) Zbl 1518.35698 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 39, No. 3, 529-573 (2022). Reviewer: Paolo Luzzini (Padova) MSC: 35R35 35J20 47A75 49Q10 35B65 PDFBibTeX XMLCite \textit{D. Mazzoleni} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 39, No. 3, 529--573 (2022; Zbl 1518.35698) Full Text: DOI arXiv
Générau, François; Oudet, Édouard; Velichkov, Bozhidar Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality. (English) Zbl 1506.35074 Arch. Ration. Mech. Anal. 246, No. 2-3, 561-602 (2022). MSC: 35J60 35R01 35R35 PDFBibTeX XMLCite \textit{F. Générau} et al., Arch. Ration. Mech. Anal. 246, No. 2--3, 561--602 (2022; Zbl 1506.35074) Full Text: DOI arXiv
Spolaor, Luca; Velichkov, Bozhidar On the logarithmic epiperimetric inequality for the obstacle problem. (English) Zbl 1496.35021 Math. Eng. (Springfield) 3, No. 1, Paper No. 4, 42 p. (2021). MSC: 35A23 35J86 PDFBibTeX XMLCite \textit{L. Spolaor} and \textit{B. Velichkov}, Math. Eng. (Springfield) 3, No. 1, Paper No. 4, 42 p. (2021; Zbl 1496.35021) Full Text: DOI arXiv
Colombo, Maria; Spolaor, Luca; Velichkov, Bozhidar Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem. (English) Zbl 1477.35317 Interfaces Free Bound. 23, No. 2, 159-167 (2021). MSC: 35R35 35B44 35J86 49J40 PDFBibTeX XMLCite \textit{M. Colombo} et al., Interfaces Free Bound. 23, No. 2, 159--167 (2021; Zbl 1477.35317) Full Text: DOI arXiv
De Philippis, Guido; Spolaor, Luca; Velichkov, Bozhidar Regularity of the free boundary for the two-phase Bernoulli problem. (English) Zbl 1473.35664 Invent. Math. 225, No. 2, 347-394 (2021). Reviewer: Adrian Muntean (Karlstad) MSC: 35R35 49Q10 47A75 35B65 PDFBibTeX XMLCite \textit{G. De Philippis} et al., Invent. Math. 225, No. 2, 347--394 (2021; Zbl 1473.35664) Full Text: DOI arXiv
Guarino Lo Bianco, Serena; La Manna, Domenico Angelo; Velichkov, Bozhidar A two-phase problem with Robin conditions on the free boundary. (Un problème à frontière libre à deux phases avec conditions au bord de Robin.) (English. French summary) Zbl 1453.35200 J. Éc. Polytech., Math. 8, 1-25 (2021). MSC: 35R35 35B65 35J86 35J25 49Q10 PDFBibTeX XMLCite \textit{S. Guarino Lo Bianco} et al., J. Éc. Polytech., Math. 8, 1--25 (2021; Zbl 1453.35200) Full Text: DOI arXiv
Colombo, Maria; Spolaor, Luca; Velichkov, Bozhidar On the asymptotic behavior of the solutions to parabolic variational inequalities. (English) Zbl 1452.35033 J. Reine Angew. Math. 768, 149-182 (2020). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35B40 35K86 49J40 PDFBibTeX XMLCite \textit{M. Colombo} et al., J. Reine Angew. Math. 768, 149--182 (2020; Zbl 1452.35033) Full Text: DOI arXiv
Engelstein, Max; Spolaor, Luca; Velichkov, Bozhidar Uniqueness of the blowup at isolated singularities for the Alt-Caffarelli functional. (English) Zbl 1448.35583 Duke Math. J. 169, No. 8, 1541-1601 (2020). MSC: 35R35 35J20 35J60 PDFBibTeX XMLCite \textit{M. Engelstein} et al., Duke Math. J. 169, No. 8, 1541--1601 (2020; Zbl 1448.35583) Full Text: DOI arXiv Euclid
Mazzoleni, Dario; Terracini, Susanna; Velichkov, Bozhidar Regularity of the free boundary for the vectorial Bernoulli problem. (English) Zbl 1445.35342 Anal. PDE 13, No. 3, 741-764 (2020). MSC: 35R35 35J60 49K10 49Q20 PDFBibTeX XMLCite \textit{D. Mazzoleni} et al., Anal. PDE 13, No. 3, 741--764 (2020; Zbl 1445.35342) Full Text: DOI arXiv
Spolaor, Luca; Trey, Baptiste; Velichkov, Bozhidar Free boundary regularity for a multiphase shape optimization problem. (English) Zbl 1430.35279 Commun. Partial Differ. Equations 45, No. 2, 77-108 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 35R35 49Q10 49N60 47A75 PDFBibTeX XMLCite \textit{L. Spolaor} et al., Commun. Partial Differ. Equations 45, No. 2, 77--108 (2020; Zbl 1430.35279) Full Text: DOI arXiv
Russ, Emmanuel; Trey, Baptiste; Velichkov, Bozhidar Existence and regularity of optimal shapes for elliptic operators with drift. (English) Zbl 1428.49044 Calc. Var. Partial Differ. Equ. 58, No. 6, Paper No. 199, 59 p. (2019). MSC: 49Q10 35R35 47A75 PDFBibTeX XMLCite \textit{E. Russ} et al., Calc. Var. Partial Differ. Equ. 58, No. 6, Paper No. 199, 59 p. (2019; Zbl 1428.49044) Full Text: DOI arXiv
Colombo, Maria; Spolaor, Luca; Velichkov, Bozhidar A logarithmic epiperimetric inequality for the obstacle problem. (English) Zbl 1428.49042 Geom. Funct. Anal. 28, No. 4, 1029-1061 (2018). MSC: 49N60 35J20 35R35 49J40 PDFBibTeX XMLCite \textit{M. Colombo} et al., Geom. Funct. Anal. 28, No. 4, 1029--1061 (2018; Zbl 1428.49042) Full Text: DOI arXiv
Bucur, Dorin; Fragalà, Ilaria; Velichkov, Bozhidar; Verzini, Gianmaria On the honeycomb conjecture for a class of minimal convex partitions. (English) Zbl 1396.52024 Trans. Am. Math. Soc. 370, No. 10, 7149-7179 (2018). MSC: 52C20 51M16 65N25 49Q10 PDFBibTeX XMLCite \textit{D. Bucur} et al., Trans. Am. Math. Soc. 370, No. 10, 7149--7179 (2018; Zbl 1396.52024) Full Text: DOI arXiv
Buttazzo, Giuseppe; Velichkov, Bozhidar A shape optimal control problem with changing sign data. (English) Zbl 1391.49079 SIAM J. Math. Anal. 50, No. 3, 2608-2627 (2018). MSC: 49Q10 49K45 PDFBibTeX XMLCite \textit{G. Buttazzo} and \textit{B. Velichkov}, SIAM J. Math. Anal. 50, No. 3, 2608--2627 (2018; Zbl 1391.49079) Full Text: DOI arXiv
De Philippis, Guido; Lamboley, Jimmy; Pierre, Michel; Velichkov, Bozhidar Regularity of minimizers of shape optimization problems involving perimeter. (English. French summary) Zbl 1381.49044 J. Math. Pures Appl. (9) 109, 147-181 (2018). Reviewer: Andrew Bucki (Edmond) MSC: 49Q10 49N60 35P99 35R35 PDFBibTeX XMLCite \textit{G. De Philippis} et al., J. Math. Pures Appl. (9) 109, 147--181 (2018; Zbl 1381.49044) Full Text: DOI arXiv
Mazzoleni, Dario; Terracini, Susanna; Velichkov, Bozhidar Regularity of the optimal sets for some spectral functionals. (English) Zbl 1368.49047 Geom. Funct. Anal. 27, No. 2, 373-426 (2017). Reviewer: Andrew Bucki (Edmond) MSC: 49Q10 35R35 47A75 49R05 49L25 PDFBibTeX XMLCite \textit{D. Mazzoleni} et al., Geom. Funct. Anal. 27, No. 2, 373--426 (2017; Zbl 1368.49047) Full Text: DOI arXiv
De Philippis, Guido; Mészáros, Alpár Richárd; Santambrogio, Filippo; Velichkov, Bozhidar \(BV\) estimates in optimal transportation and applications. (English) Zbl 1333.49051 Arch. Ration. Mech. Anal. 219, No. 2, 829-860 (2016). MSC: 49N60 49Q20 49K20 35K55 90B20 PDFBibTeX XMLCite \textit{G. De Philippis} et al., Arch. Ration. Mech. Anal. 219, No. 2, 829--860 (2016; Zbl 1333.49051) Full Text: DOI arXiv
Bucur, D.; Velichkov, B. A free boundary approach to shape optimization problems. (English) Zbl 1353.49052 Philos. Trans. A, R. Soc. Lond. 373, No. 2050, Article ID 20140273, 15 p. (2015). MSC: 49Q10 35R35 49R05 35J20 PDFBibTeX XMLCite \textit{D. Bucur} and \textit{B. Velichkov}, Philos. Trans. A, R. Soc. Lond. 373, No. 2050, Article ID 20140273, 15 p. (2015; Zbl 1353.49052) Full Text: DOI
Buttazzo, Giuseppe; Oudet, Edouard; Velichkov, Bozhidar A free boundary problem arising in PDE optimization. (English) Zbl 1342.49004 Calc. Var. Partial Differ. Equ. 54, No. 4, 3829-3856 (2015). Reviewer: Shlomo Carmi (Baltimore) MSC: 49J20 49J45 49Q10 49Q20 35R35 49M05 35J25 74C05 PDFBibTeX XMLCite \textit{G. Buttazzo} et al., Calc. Var. Partial Differ. Equ. 54, No. 4, 3829--3856 (2015; Zbl 1342.49004) Full Text: DOI arXiv
van den Berg, Michiel; Buttazzo, Giuseppe; Velichkov, Bozhidar Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity. (English) Zbl 1329.49095 Pratelli, Aldo (ed.) et al., New trends in shape optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-17562-1/hbk; 978-3-319-17563-8/ebook). ISNM. International Series of Numerical Mathematics 166, 19-41 (2015). MSC: 49Q10 49R05 PDFBibTeX XMLCite \textit{M. van den Berg} et al., ISNM, Int. Ser. Numer. Math. 166, 19--41 (2015; Zbl 1329.49095) Full Text: DOI arXiv
Brasco, Lorenzo; De Philippis, Guido; Velichkov, Bozhidar Faber-Krahn inequalities in sharp quantitative form. (English) Zbl 1334.49149 Duke Math. J. 164, No. 9, 1777-1831 (2015). Reviewer: Manuel Ritoré (Granada) MSC: 49R05 49Q20 49Q10 47A75 PDFBibTeX XMLCite \textit{L. Brasco} et al., Duke Math. J. 164, No. 9, 1777--1831 (2015; Zbl 1334.49149) Full Text: DOI arXiv Euclid
Bucur, Dorin; Mazzoleni, Dario; Pratelli, Aldo; Velichkov, Bozhidar Lipschitz regularity of the eigenfunctions on optimal domains. (English) Zbl 1319.49067 Arch. Ration. Mech. Anal. 216, No. 1, 117-151 (2015). Reviewer: Chie-Ping Chu (Taipei) MSC: 49Q10 49R05 35R35 PDFBibTeX XMLCite \textit{D. Bucur} et al., Arch. Ration. Mech. Anal. 216, No. 1, 117--151 (2015; Zbl 1319.49067) Full Text: DOI arXiv
Buttazzo, Giuseppe; Gerolin, Augusto; Ruffini, Berardo; Velichkov, Bozhidar Optimal potentials for Schrödinger operators. (Potentiels optimaux pour les opérateurs de Schrödinger.) (English. French summary) Zbl 1306.49018 J. Éc. Polytech., Math. 1, 71-100 (2014). MSC: 49J45 35J10 49R05 35P15 35J05 PDFBibTeX XMLCite \textit{G. Buttazzo} et al., J. Éc. Polytech., Math. 1, 71--100 (2014; Zbl 1306.49018) Full Text: DOI arXiv
De Philippis, Guido; Velichkov, Bozhidar Existence and regularity of minimizers for some spectral functionals with perimeter constraint. (English) Zbl 1297.49077 Appl. Math. Optim. 69, No. 2, 199-231 (2014). MSC: 49Q10 49N60 PDFBibTeX XMLCite \textit{G. De Philippis} and \textit{B. Velichkov}, Appl. Math. Optim. 69, No. 2, 199--231 (2014; Zbl 1297.49077) Full Text: DOI arXiv
Velichkov, Bozhidar A note on the monotonicity formula of Caffarelli-Jerison-Kenig. (English) Zbl 1297.49066 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 25, No. 2, 165-189 (2014). MSC: 49N60 49J20 35B65 35R35 PDFBibTeX XMLCite \textit{B. Velichkov}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 25, No. 2, 165--189 (2014; Zbl 1297.49066) Full Text: DOI
Bucur, Dorin; Buttazzo, Giuseppe; Velichkov, Bozhidar Spectral optimization problems with internal constraint. (English) Zbl 1287.49049 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 3, 477-495 (2013). MSC: 49R05 49J45 49Q10 35P15 47A75 35J25 PDFBibTeX XMLCite \textit{D. Bucur} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 3, 477--495 (2013; Zbl 1287.49049) Full Text: DOI arXiv