Research Publications of Achilles Tertikas

In reverse chronological order.

• Liouville type properties for a class of weighted anisotropic  elliptic equations,
  with Stathis Filippas and Luisa Moschini (2024) (submitted).

• Best constants for weighted  Hardy inequalities in the exterior of balls and circular cylinders,
  with  Stathis Filippas (2024) (submitted).

• Sobolev improvements on sharp Rellich inequalities,
  with Gerassimos Barbatis, J. Spectr. Theory 14 (2024), 641--663.

• Heat and Martin kernel estimates for Schrödinger operators with critical Hardy potentials,
  with Gerassimos Barbatis and Konstantinos T. Gkikas,   Math.  Annalen 389 (2024), 2123--2192 .

• Best Sobolev constants in the presence of sharp Hardy terms in Euclidean and hyperbolic space,
  with Gerassimos Barbatis,   Bull. Hellenic Math. Soc.  63 (2019), 64--96 .

• Sharp Hardy and Hardy--Sobolev inequalities with point singularities on the boundary,
  with Gerassimos Barbatis and Stathis Filippas,     J. Math. Pures Appl  117 (2018), 146--184.

• Correction to: Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian,
  with Stathis Filippas and Luisa Moschini,    Arch. Rational Mech. Anal.  229 (2018), 1281--1286.

• Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities,
  with Jean Dolbeault, Maria J. Esteban and Stathis Filippas,  Calc. Var. Partial Differential Equations   54 (2015), 2465--2481.

• On the Hardy constant of some non-convex planar domains,
  with Gerassimos Barbatis,  "Geometric Methods in PDE's",  Springer INdAM vol. 13, Citti, G., Manfredini, M.,
  Morbidelli, D., Polidoro, S., Uguzzoni, F., (2015), 15--41.

• Trace Hardy--Sobolev--Mazy'a inequalities for the half fractional Laplacian,
  with Stathis Filippas and Luisa Moschini,  Com. Pure Applied Anal. 14(2) (2015), 373--382.

• On the Hardy constant of non-convex planar domains: the case of the quadrilateral,
  with Gerassimos Barbatis,  J. Funct. Anal.  266 (2014),  3701--3725.
  

• Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian,
  with Stathis Filippas and Luisa Moschini, Arch. Rational Mech. Anal. 208 (2013), 109--161.

• Radial symmetry and symmetry breaking for some interpolation inequalities,
  with Jean Dolbeault, Maria J. Esteban and Gabriella Tarantello,
  Calc. Var. Partial Differential Equations 42 (2011), 561--585.

• A logarithmic Hardy inequality,
  with Manuel del Pino, Jean Dolbeault and Stathis Filippas, J. Funct. Anal. 259 (2010), 2045--2072.

• Optimal Hardy-Sobolev-Maz'ya inequalities with multiple interior singularities,
  with Stathis Filippas and Jesper Tidblom, In: Around the research of Vladimir Maz'ya,
  A. Laptev (ed.),  Ιnternational Mathematical Series 11 (2010), 137--160.

• On the best constant of Hardy--Sobolev Inequalities,
  with Adimurthi and Stathis Filippas, Nonlinear Anal. T.M.A. 70 (2009), 2826--2833.

• Improving $L^2$ estimates to Harnack inequalities,
  with Stathis Filippas and Luisa Moschini, Proc. Lond. Math. Soc. 99 (2009), 326--352.

• On the structure of Hardy-Sobolev-Maz'ya inequalities,
  with Stathis Filippas and Jesper Tidblom, J. Eur. Math. Soc. 11 (2009), 1165--1185.

• On a class of weighted anisotropic Sobolev inequalities,
  with Stathis Filippas and Luisa Moschini, J. Funct. Anal. 255 (2008), 90--119.

• A Liouville-type theorem for the $p$-Laplacian with potential term,
  with Y. Pinchover and K. Tintarev, Ann. Inst. H. Poincare' Anal. Non Line'aire 25 (2008), 357-368.

• Sharp two--sided heat kernel estimates for critical Schr\"{o}dinger operators on bounded domains,
  with S. Filippas and L. Moschini, Comm. Math. Phys. 273 (2007), 237--281.

• Critical Hardy-Sobolev Inequalities,
  with S. Filippas and V.G. Maz'ya, J. Math. Pures Appl. 87 (2007), 37--56.

• Best constants in the Hardy-Rellich Inequalities and Related Improvements,
  with N. Zographopoulos, Adv. Math. 209,2 (2007), 407--459.

• On existence of minimizers for the Hardy-Sobolev-Maz'ya inequality,
  with K. Tintarev, Ann. Mat. Pura Appl. 186 (2007), 645--662 .

• Positive solutions of a Neumann Problem with competing critical nonlinearities,
  with J. Chabrowski and S. Filippas, Topol. Methods Non. Anal. 28 (2006), 1-31.

• On a question of Brezis and Marcus,
  with S. Filippas and V.G. Maz'ya ,  Calc. Var. Partial Differential Equations, 25,4 (2006), 491-501.

• On a class of Rellich inequalities,
  with G. Barbatis, J. Comput. Applied Math. 194 (2006), 156-172.

• Sharp Hardy-Sobolev inequalities,
  with S. Filippas and V.G. Maz'ya , Comptes Rendus Mathematique 339 (2004), no. 7, 483-486.

• Critical heat kernel estimates for Schodinger operators via Hardy-Sobolev inequalities,
  with G. Barbatis and S. Filippas, J. Funct. Anal. 208 (2004), no. 1,1--30.

• Refined geometric $\; L^p$ Hardy inequalities,
  with G. Barbatis and S. Filippas, Commun. Contemp. Math. 5 (2003), no. 6, 869--881.

• Series expansion for $\; L^p$ Hardy inequalities,
  with G. Barbatis and S. Filippas, Indiana Univ. Math. J. 52 (2003), no. 1,171--190.

• A unified approach to improved $\; L^p$ Hardy inequalities with best constants,
  with G. Barbatis and S. Filippas, Trans. Amer. Math. Soc. 356 (2004), no. 6, 2169--2196 .

• Optimizing Improved Hardy Inequalities,
  with S. Filippas, J. Funct. Anal. 192 (2002), no. 1, 186--233;
  Corrigendum, J. Funct. Anal. 255 (2008), no. 8, 2095.

• On Similarity Solutions of a Heat Equation with a Nonhomogenous Nonlinearity,
  with S. Filippas, J. Diff. Eqs. 165 (2000), no. 2, 468--492.

• Critical Phenomena in Linear Elliptic Problems,
  J. Funct. Anal. 154 (1998), no. 1, 42--66.

• A global branch of positive solutions above the continuous spectrum for problems with indefinite nonlinearities,
  with T. K\"upper, Proc. Royal Soc. Edinburgh 126A (1996), 465-482.

• Uniqueness and Nonuniqueness of positive solutions for a semilinear elliptic equation in $\; I \!\! R^n$,
  Diff. and Integral Equs 8,4 (1995), 829-848.

• The existence of principal eigenvalues for problems with indefinite weight function in $\; I \!\! R^n$,
  with K. J. Brown, Proc. Royal Soc. Edinburgh 123A (1993), 561-569.

• Graph intersection and uniqueness results for some nonlinear elliptic problems,
  with J. Toland, J. Diff. Eqs. 95,1 (1992), 154-168.

• Global bifurcation of positive solutions in $\; I \!\! R^n$,
  Nonlinear Diffusion Equations and their Equilibrium States 3, edited by N. G. Lloyd,
  W. M. Ni, L.A. Peletier and J. Serrin, in Progress in Nonlinear Differential Equations
  and their Applications 7 (1992), Birkhauser Verlag, 513-536.

• Stability and instability of positive solutions of semi-positone problems,
  Proc. Amer. Math. Soc. 114,4 (1992), 1035-1040.

• On the bifurcation of radially symmetric Steady-State solutions arising in population genetics,
  with K. J. Brown, SIAM J. Math. Anal. 22,2 (1991), 400-413.

• Existence and Nonexistence of Steady-State solutions for a selection migration model in population genetics,
  with K. J. Brown and S. S. Lin, J. Math. Biol. 27 (1989), 91-104.

• Uniqueness of solutions for problems arising in population genetics,
  in Differential Equations edited by C. M. Dafermos, G. Ladas and G. Papanicolaou,
  Lecture notes in Pure and Applied Mathematics 118 (1989), 667-672.

• Global bifurcation analysis and uniqueness for a semilinear problem,
  Proc. Roy. Soc. Edinburgh 111A (1989), 265-284.

• On an equation arising in Optical Bistability,
  with K. J. Brown, J. Math. Analysis Appl. 139 (1989), 390-407.

• Existence and Uniqueness of solutions for a Nonlinear Diffusion problem arising in Population Genetics,
  Arch. Rational Mech. Anal. 103 (1988), 289-317.