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Regularity and Pohozaev identity for the Choquard equation involving the $p$-Laplacian operator

Vincenzo Ambrosio

Abstract

In this paper, we study the regularity of weak solutions for a class of nonlinear Choquard equations driven by the $p$-Laplacian operator. We also establish a Pohozaev type identity.

Regularity and Pohozaev identity for the Choquard equation involving the $p$-Laplacian operator

Abstract

In this paper, we study the regularity of weak solutions for a class of nonlinear Choquard equations driven by the -Laplacian operator. We also establish a Pohozaev type identity.
Paper Structure (2 sections, 3 theorems, 43 equations)

This paper contains 2 sections, 3 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['thm1']}

Key Result

Theorem 1.1

LL Let $r, t\in (1, \infty)$ and $\mu\in (0, N)$ with $\frac{1}{r}+\frac{\mu}{N}+\frac{1}{t}=2$. Let $f\in L^{r}(\mathbb{R}^{N})$ and $h\in L^{t}(\mathbb{R}^{N})$. Then there exists a sharp constant $C(N, \mu, r)>0$, independent of $f$ and $h$, such that

Theorems & Definitions (4)

  • Theorem 1.1
  • Theorem 1.2
  • Remark 2.1
  • Lemma 2.1