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Regularity for the fractional logarithmic -Laplacian
Nirjan Biswas, Stuti Das, Abhrojyoti Sen
The paper establishes a Harnack inequality with tail terms and local Hölder continuity for the fractional logarithmic p‑Laplacian, a nonlocal operator obtained by differentiating t…
Harnack inequality for mixed local-nonlocal weighted homogeneous equations
Nirjan Biswas, Stuti Das
We consider the following class of mixed local-nonlocal equations: \begin{equation}\tag{P}\label{eq:P} -Î_p u + (-Î)_p^s u = V |u|^{p-2}u \text{ in } Ω, \end{equation} where $s…
Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data
Stuti Das
This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular non…
Regularity results for a class of mixed local and nonlocal singular problems involving distance function
Kaushik Bal, Stuti Das
We investigate the following mixed local and nonlocal quasilinear equation with singularity given by \begin{eqnarray*} \begin{split} -Î_pu+(-Î)_q^s u&=\frac{f(x)}{u^δ}\text { in…
Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity
Kaushik Bal, Stuti Das
We will prove multiplicity results for the mixed local-nonlocal elliptic equation of the form \begin{eqnarray} \begin{split} -Î_pu+(-Î)_p^s u&=\fracλ{u^γ}+u^r \text { in } Ω,…