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Ankur Pandey

Publications and source records attributed to Ankur Pandey.

3 recordsLinked to original sources
arXiv2025

Logarithmic double phase embeddings with variable exponents: Necessary and Sufficient Conditions

In this paper, we study the necessary and sufficient conditions in the domain for Sobolev-type embedding of the space $W^{1,\Phi(\cdot,\cdot)}(\Omega)$ where $\Phi(x,t):=t^{p(x)}+ a(x) t^{q(x)}\log^{r(x)}(e+t)$ with $1\leq p(x)\leq q(x).$ We have established subcritical embedding in bounded John domains under some regularity assumptions on exponents $p,$ $q,$ $r$, and $a$. Conversely, we have proved that if the embedding holds in any domain $\Omega$ in $\mathbb{R}^n,$ then $\Omega$ must satisfy the log-measure density condition.

math.FA↗
arXiv2025

Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces

In this paper, we show that sets with zero Sobolev $p(\cdot)$-capacity have generalized Hausdorff $h(\cdot)$-measure zero, for some gauge function $h(\cdot).$ We also prove that sets with zero Musielak-Orlicz-Sobolev $\Phi(\cdot,\cdot)$-capacity, for a particular class of functions $\Phi(\cdot,\cdot),$ have generalized Hausdorff $h(\cdot)$-measure zero, for a suitable gauge function $h(\cdot).$

math.FA↗