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Regularity for the fractional logarithmic -Laplacian
Nirjan Biswas, Stuti Das, Abhrojyoti Sen
We prove the Harnack inequality (with tails) and local Hölder regularity for the fractional logarithmic -Laplace operator, which is derived by differentiating the fractional …
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} -Δ_p u + (-Δ)_p^s u = V |u|^{p-2}u \text{ in } Ω, \end{equation} where $s \in…
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} -Δ_pu+(-Δ)_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} -Δ_pu+(-Δ)_p^s u&=\fracλ{u^γ}+u^r \text { in } Ω, \\u&>…
On a mixed local-nonlocal evolution equation with singular nonlinearity
Kaushik Bal, Stuti Das
We will prove several existence and regularity results for the mixed local-nonlocal parabolic equation of the form \begin{eqnarray} \begin{split} u_t-Δu+(-Δ)^s u&=\frac{f(x,t)}{u^{…
Gradient Hölder regularity in mixed local and nonlocal linear parabolic problem
Stuti Das
We prove the local Hölder regularity of weak solutions to the mixed local nonlocal parabolic equation of the form \begin{equation*} u_t-Δu+\text{P.V.}\int_{\mathbb{R}^{n}} {\frac{u…