Research Publications of Achilles Tertikas

In reverse chronological order.

• Sharp Trace  Hardy-Sobolev-Maz'ya Inequalities  and the Fractional Laplacian,
  with  Stathis Filippas and Luisa Moschini,    preprint (2011).
  

• 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.), 137--160, International Mathematical Series 11 (2010).

• 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.