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Trudinger-type inequalities in RN with radial increasing mass-weight

  • Cristina Tarsi
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Potentials and Partial Differential Equations
This chapter is in the book Potentials and Partial Differential Equations

Abstract

We prove Trudinger-type inequalities with radial increasing mass-weights in the whole ℝN , in the setting of mass-weighted Sobolev spaces W1,Nw (ℝN ). Due to the presence of increasing weights, we will not apply symmetrization tools: the proofs of our inequalities mainly rely on a proper transformation of variables, which allows us to reduce the weighted case to the unweighted classical one.

Abstract

We prove Trudinger-type inequalities with radial increasing mass-weights in the whole ℝN , in the setting of mass-weighted Sobolev spaces W1,Nw (ℝN ). Due to the presence of increasing weights, we will not apply symmetrization tools: the proofs of our inequalities mainly rely on a proper transformation of variables, which allows us to reduce the weighted case to the unweighted classical one.

Chapters in this book

  1. Frontmatter I
  2. Foreword V
  3. Contents VII
  4. Yau’s conjecture on the dimension of harmonic polynomials 1
  5. On Carrasco Piaggio’s theorem characterizing quasisymmetric maps from compact doubling spaces to Ahlfors regular spaces 23
  6. On trace theorems for weighted mixed-norm Sobolev spaces and applications 49
  7. Sharp stability of the logarithmic Sobolev inequality in the critical point setting 77
  8. On a variational problem of nematic liquid crystal droplets 103
  9. Estimates for the variable order Riesz potential with applications 127
  10. A remark on the atomic decomposition in Hardy spaces based on the convexification of ball Banach spaces 157
  11. A Bliss–Adams inequality 179
  12. Trudinger-type inequalities in RN with radial increasing mass-weight 197
  13. In response to David R. Adams’ October 12, 2001, letter 215
  14. Some remarks on capacitary integrals and measure theory 235
  15. Remarks on vector-valued Gagliardo and Poincaré–Sobolev-type inequalities with weights 265
  16. Index 287
https://doi.org/10.1515/9783110792720-009

Chapters in this book

  1. Frontmatter I
  2. Foreword V
  3. Contents VII
  4. Yau’s conjecture on the dimension of harmonic polynomials 1
  5. On Carrasco Piaggio’s theorem characterizing quasisymmetric maps from compact doubling spaces to Ahlfors regular spaces 23
  6. On trace theorems for weighted mixed-norm Sobolev spaces and applications 49
  7. Sharp stability of the logarithmic Sobolev inequality in the critical point setting 77
  8. On a variational problem of nematic liquid crystal droplets 103
  9. Estimates for the variable order Riesz potential with applications 127
  10. A remark on the atomic decomposition in Hardy spaces based on the convexification of ball Banach spaces 157
  11. A Bliss–Adams inequality 179
  12. Trudinger-type inequalities in RN with radial increasing mass-weight 197
  13. In response to David R. Adams’ October 12, 2001, letter 215
  14. Some remarks on capacitary integrals and measure theory 235
  15. Remarks on vector-valued Gagliardo and Poincaré–Sobolev-type inequalities with weights 265
  16. Index 287
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