# Sobolev-type regularity and Pohozaev-type identities for some degenerate and singular problems

@inproceedings{Felli2022SobolevtypeRA, title={Sobolev-type regularity and Pohozaev-type identities for some degenerate and singular problems}, author={Veronica Felli and Giovanni Siclari}, year={2022} }

on the bottom of a half (N + 1)-dimensional ball. The interest in such a type of equations and related regularity issues has developed starting from the pioneering paper [7], proving local Hölder continuity results and Harnack’s inequalities, and has grown significantly in recent years stimulated by the study of the fractional Laplacian in its realization as a Dirichlet-to-Neumann map [3]. In this context, among recent regularity results for problems of type (1)–(2), we mention [2] and [12] for…

## References

SHOWING 1-10 OF 22 REFERENCES

### Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions

- Mathematics
- 2020

Abstract We consider a class of equations in divergence form with a singular/degenerate weight Under suitable regularity assumptions for the matrix A and f (resp. F) we prove Hölder continuity of…

### Weighted Sobolev spaces and capacity.

- Mathematics
- 1994

Let Ω be an open set in R and 1 < p < ∞ . In this paper we consider the theory of weighted Sobolev spaces H with weight function in Muckenhoupt’s Ap -class. Our main purpose is to provide a coherent…

### A First Course in Sobolev Spaces

- Mathematics
- 2009

Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural…

### Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions

- Mathematics
- 2020

We consider a class of equations in divergence form with a singular/degenerate weight $$ -\mathrm{div}(|y|^a A(x,y)\nabla u)=|y|^a f(x,y)+\textrm{div}(|y|^aF(x,y))\;. $$ Under suitable regularity…

### Unique continuation principles for a higher order fractional Laplace equation

- MathematicsNonlinearity
- 2020

In this paper we prove the strong unique continuation principle and the unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open…

### Nonlinear equations for fractional Laplacians I: Regularity, maximum principles, and Hamiltonian estimates

- Mathematics
- 2010

### Elliptic Problems in Nonsmooth Domains

- Mathematics
- 1985

Foreword Preface 1. Sobolev spaces 2. Regular second-order elliptic boundary value problems 3. Second-order elliptic boundary value problems in convex domains 4. Second-order boundary value problems…

### Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations

- Mathematics
- 2013

Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up…

### An Extension Problem Related to the Fractional Laplacian

- Mathematics
- 2007

The operator square root of the Laplacian (− ▵)1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the…