What question did this study set out to answer?

The aim is to prove the existence of weak radially symmetric solutions for a specific Dirichlet problem.

March 31, 2026Siberian Mathematical Journal0 citations

On Radially Symmetric Solutions to the Dirichlet Problem for an Elliptic Equation with the p (|x|) -Laplacian

ATAr. S. TersenovSobolev Institute of Mathematics RSR. Ch. SafarovNovosibirsk State University

Key Points

The aim is to prove the existence of weak radially symmetric solutions for a specific Dirichlet problem.
Studied an elliptic equation involving the p(|x|)-Laplacian
Analyzed conditions related to lower-order terms
Assumed p(|x|) is continuously differentiable and nonincreasing
Proved existence of weak radially symmetric solutions
Demonstrated that the derivative of solutions is Hölder continuous

Abstract

We study the Dirichlet problem for an elliptic equation with the p (|x|) -Laplacian and lower-order terms that do not satisfy the Bernstein–Nagumo condition. Under the assumption that p (|x|) is a continuously differentiable nonincreasing function, we prove the existence of a weak radially symmetric solution whose derivative is Hölder continuous.

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